With my two older sisters, we'd hang back behind my English-poor pappou (grandfather) and wait for him to shave off the newest layer of crispy meat and tip it into a nearby tray.
Then, slowly, silently, we'd edge in like vultures and pluck up a handful of hot yiros and retreat.
Sometimes we became greedy and earned an indecipherable rebuke, with accompanying finger wag.
Language might have been a barrier, but we knew that metronomic back-and-forth of pappou's index finger was the international sign for: "Oi! Scram!"
These days, I get my yiros fix from more welcoming outlets.
In Melbourne, endearingly traditional spots like Hellenic Bite on Swan Street (replete with white rendered walls and Mediterranean murals) and Stalactites on the Lonsdale Street strip serve up reliably good fare.
The latter is well-known for being a 24-hour venue - meaning that if you, like me, manage to find yourself craving taramasalata after a night out, it can be sated.
A few doors down is International Cakes, a diner that offers up generous wedges of baklava and semolina cake that gives my yiayia's - "grandmother" in Greek - a run for its money.
For something a bit more formal, there's always Agapi on Swan Street. A Richmond fixture, the name means "my love", and can easily describe the whole menu.
Given modern trends to fuse cuisines, there's something comforting about Agapi's line-up of traditional dishes - grilled calamari, vine-wrapped dolmadakia, moussaka and stuffed peppers.
In a similar vein, Pireaus Blues on Brunswick Street hums with the energetic vibe of a regular Hellenic haunt.
Proclaiming to be Melbourne's "most authentic Greek restaurant", its packed interior is typically filled with the sound of loud conversations and wafts of fried eggplant.
In recent times, Melbourne's humble souvlaki has also been given a overdue makeover courtesy of the endlessly enterprising George Calombaris.
Jimmy Grants opened earlier in the year, plonked conveniently between the trendy urban strips of Brunswick and Smith streets.
A recent visit proved business is still booming, with the eatery's cosy dining space crowded with a mix of Greek families and tourists.
Highly recommended is the delicious dish called "Mr Papadopoulos souva" - melt-in-your-mouth lamb yiros wrapped in warm pita, with caramelised onions, fresh parsley and lashings of mustard aioli.
A serving of chips doesn't hurt either, but no tomato sauce here, only crumbled feta, oregano and garlic oil.
For dessert, it's pretty hard to go past Greek yoghurt ice-cream, encased in white chocolate.
The whole thing is a very clever concept, and one that tastefully injects some historical clout into the takeaway scene. Say the name quickly enough, and you'll see why the joint's tagline is "there's a little bit of Jimmy in all of us".
And with souvas under 10 bucks, maybe I'll get one for my pappou next time.
I do owe him, after all.
UNDERSTANDING GREEK FOOD
Yiros - Typically lamb, but also applies to any meat roasted on a spit.
Taramasalata - A dip made from fish roe, often blended with potatoes or bread crumbs.
Baklava - Nut-filled pastry, soaked in sugar syrup.
Semolina cake - Dense semolina cake soaked in sugar syrup.
Dolmadakia - Vine-wrapped fingers filled with rice and vegetables.
Moussaka - Meat dish layered with eggplant.
IF YOU GO
Staying there: The Mercure Melbourne Treasury Gardens is conveniently located on the fringes of the Treasury Gardens, at the top of the city grid.
Stalactites, 177-183 Lonsdale Street, CBD (stalactites.com.au).
The writer travelled at her own expense.