"A mate of mine said, 'Peter, what are you going to do if you're going to be a bachelor again? I said, 'I suppose I'm going to have to exchange the tea bags in my wallet for condoms again.'"
It was a half-hearted joke, and one that seemed to be made mostly out of habit. Over the years, he has developed a reputation as a ladies' man. There is a fair amount of evidence, much of it his own evidence, for that reputation, which he says is unwarranted.
In his autobiography, he writes: "When [second wife] Catherine decided to settle down in the Waikato, leaving me living some of the time in Auckland, it was inevitable that I would sooner or later have woman trouble."
Elsewhere in the book, he recounts meeting an attractive woman at a gallery opening: "In my usual raffish manner," he writes, "I had given her my personal card and invited her to call on my Parnell residence whenever she might be in town or passing by."
At another, more recent, art gallery thing, he meets a woman who reminds him that nearly 40 years before, they had spent a weekend together "drowning in champagne" in the honeymoon suite at the Hermitage at Mt Cook, after the launch of his first book, on his British publisher's coin. He has absolutely no recollection of it, but does not seem to doubt it. Immediately preceding this story is a line in which he says he's, "flummoxed as to why everybody presumes I've led a debauched sort of life". Only a couple of minutes after arriving to meet me at The Alphabet Cafe in Parnell, he spotted a woman sitting alone in the corner, and he leaned over to the publicist and whispered something. The publicist looked over at the woman, then back at me and said, "I knew I should have done a sweep before we arrived."
When the woman left a few minutes later, she and Bromhead exchanged a perfunctory greeting. Bromhead looked back at me and raised a knowing eyebrow.
His former editor at the Auckland Star, Judy McGregor, says that his persona in the newsroom was "flirty", but that he was never patronising to women in senior editorial roles at a time when that was novel, and she could not remember a single sexist cartoon of his.
Asked outright about his raffish reputation, he says: "If half the mythology about me was true in that aspect, I'd be very grateful. Most of that is pure mythology. Obviously I've had a few adventures over the years but in the main, so much really is just simply bollocks."
Regardless, whatever has happened in the past is no indicator of what will happen in the future.
"It's just too much bother. I always used to have flash cars, XK Jaguar convertibles and flash Mercedes and all that stuff. Now I drive a little Skoda Fabia because I don't give a toss, and I've got an old truck. That's all I ever want in my life. And as far as women are concerned, I enjoy talking to women but I don't want any more children, so ... "
Fairly early in my meeting with Bromhead, he announced that he likes to test people's senses of humour by quoting cartoons at them. I tensed, sensing that this attempted translation of visual into verbal humour was not a good idea, but there was no time to protest because almost immediately he was doing it.
He is such an institution at the Alphabet Cafe that, 10 years ago, he drew himself on the blackboard there, with the accompanying text, "I come here!" and that drawing is still there, several changes of owner and a lot of re-chalking later.
He began. It was a cartoon from The New Yorker: "Two small dogs, sitting on a couch. And in front of them is a little coffee table, and on the coffee table is a little traditional dog kennel, a tiny one, matchbox size. And one dog, he's got his arm round the other dog and he's saying to the dog, it's only the architect's model but I'm very excited."
There was silence. I didn't get it. I tried to get it, but I couldn't, and as the silence extended, I could no longer think about what might be funny about the cartoon, but only about the discomfort of the silence.
"About the little dog kennel," Bromhead said, unhelpfully, trying to escort me to a place of understanding.
"Okay," I said, not reaching that place.
"It's only the architect model but I'm very excited," he added. "That, to me, is a funny cartoon."
"Why am I not getting it?" I asked. "Is it because I'm dumb?"
"Yes," he said. "You are dumb." I laughed, although nothing about his demeanour indicated that he was joking.
"Well," he went on, "traditionally in architecture, they often build a model of a house and people get excited about that. In this case, it's two dogs talking about a very traditional dog kennel. It's a pun on the adult version. For me, that is an amusing cartoon."
Long after the interview was finished, still unable to grasp the cartoon, I looked it up online. On seeing it, I got it instantly. The dogs were dressed in fancy clothes, drinking wine and cocktails and looking at this model of a doghouse on their lovely modern coffee table. It was their apartment! They were wealthy dogs, in their own luxury apartment, and they were getting excited about the architect's plans for a kennel. It was funny!
When I was listening to Bromhead tell it, I had the picture all wrong. I had imagined the dogs as pets, wearing collars not clothes, sitting not on their own couch but that of their owners. That version hadn't been funny.
Understanding what's happening in somebody else's head is the most difficult of puzzles.
Bromhead didn't start cartooning until he was well into his 30s. He moved to a small South Auckland farmhouse and set up a studio, where he spent most of his day drawing cartoons and sending them to various publications, where they were invariably rejected. He doesn't really know why he did it, except for an "urge to be creative in a practical manner", and it was a year before he had any success at all.
He started at the Auckland Star in 1968 and says they were soon paying him $75,000 a year for about two hours' work a day. "I estimated that, based on an hourly rate," he writes in his autobiography, "I was close to being the highest paid executive in the country." He would finish at the Star mid-morning, then go over to an office he rented for $25 a week on Queen St, where he would work on his design business.
That business turned over $1 million in its first year and then really took off, gathering clients in Australia, Canada and Switzerland, doing furnishing fit-outs in Auckland for the likes of the brand new Aotea Centre and for the newly created Telecom. The business grew to a peak of more than 30 employees, with turnover of about $50 million a year.
The design business is still going but, in spite of the financial rewards it has brought him, which once allowed him to donate "a few hundred thousand" to start up a corporate tennis tournament, he thinks of himself primarily as a cartoonist. He still does three cartoons a week for the Herald.
Herald cartoonist Rod Emmerson compares him to the legendary Australian newspaper cartoonist Bruce Petty: "Although their styles are worlds apart," Emmerson says, "it's the depth of the intellectual component and the use of almost floating surreal scenes where their work collides. His bone-dry wit and power of observation are the sharpest knives in his tool box."
Bromhead's pick of all his cartoons is one that ran in the Star in the mid-1980s. It showed a young man sniffing glue on the steps of a monument reading, "They died so you can live". It shows the futility of belief, he says.
Another favourite depicts a zombified family sitting on a couch in front of a television set, the screen of which is taken up by the words "Book Week". He says it shows "technology reminding us of the former golden age and today's dumbed-down family trying to grasp what it means."
It might be stretching things to try to analyse a whole life, or even a career, through the intense zoom lens of just two cartoons, but it's interesting how thematically similar these two are: rose-coloured reimaginings of the past and bleak, pessimistic views of the present. Neither of them makes you laugh.
