What Birnbaum did instead was try to find out everything she could about the inner workings of the nose - how we smell, why we smell and what it means for us.
Relentlessly curious, she meets other sufferers of anosmia (the clinical term for the lack of ability to perceive smells), talks to doctors, scientists and perfumers, and begins to understand the breadth of her loss.
She can't smell danger, a lover's skin or any of the scents that link her to her past. Even the memory of smell eludes her.
"The absence of smell for me was a vicious monotone thing," she tells us. "I began to see how for others, too, it could leave depression and anxiety, disordered eating, and a lack of sexual desire. Something much deeper than the thick, salt-fat scent of a chicken roasting in the kitchen is lost without the ability to smell."
But when Birnbaum attempts to cook again there's a faint whiff of something. It smells of the woods and Earth, is pungent and warm. It's rosemary.
She embarks on a mission to regain her sense of smell. It happens very slowly and is weird at times - at one point she thinks she can smell her own brain.
But with extraordinary tenacity she follows every lead in the hope of a cure. She visits a pioneering flavour laboratory, meets writer and neurologist Oliver Sacks, and even enrols at a perfume school in Grasse, France, which seems extreme but it's there that Birnbaum realises it is possible to train herself to smell again.
Is she cured by the end? Who knows. This is one of the more mysterious areas of science and, though she can smell almost everything today, what Birnbaum doesn't know is if they smell exactly the same way to her now as they used to.
Her olfactory exploration makes for fascinating reading. She comes across as a fairly intense person, as well as a smart, interesting, often quite journalistic writer who manages to pack a lot of science into Season To Taste, while still keeping things lively.
The result is part food memoir, part love story but mostly the record of a young woman battling adversity and trying to find her way in life. I found it inspirational, honest and engrossing.
Season To Taste is a book to get you thinking - and smelling - more.