There’s a radio commercial running hereabouts for a brand of pasta in which the “narrator” (presumably a chef) talks about visiting restaurants in every region in Italy where he (this is a near-exact quote) “memorized the flavor and aroma of each dish, down to the last ingredient…I call this my taste memory”, implying he can discern the recipe by taste. Is this actually possible?
It almost sounds like the guy is saying his tastebuds have some kind of memory chip. 
But, to be serious:
If this guy was an actual trained chef, his palate is going to be more refined than your average person. As a part of culinary training, one of the things that a chef must rely on is his ingredient identification (a thing that I found that I’ve been tested on over & over again in culinary school). A chef needs to be able to distinguish what is part of a dish that gives it its particular flavors.
Considering that a main part of the tasting ability in humans is also the sense of smell–and that the sense of smell is the most powerful of senses–it is possible that a chef can have something along the lines of “taste memory”.
One of the types of memory is is theorized we have is what’s called sensory memory. It’s pretty much what it sounds like it is-- the memory of information we get from our senses. My grandmother’s old house in the valley, for example, had a very distinct scent. When you walked in, it was the first thing you noticed. It was a nice smell, almost like a combination of freshly turned earth and clean sheets. We used to go over at least once a week, but I haven’t been to that house in about ten years now. I still remember the smell though; if you blindfolded me and took me to that house without my knowledge, I’d be able to identify where I was by that scent alone.
So yeah, I think it’s possible that a person can became so thoroughly familiar with the tastes and aromas of a particular dish that he can discern its tastes and aromas from other identical dishes.
I’m often surprised when people can’t tell which (basic, at least)spices are in a dish.
What’s this? they say.
A voice inside me screams “CORIANDER! It’s frigging coriander, you dolt! There’s black pepper, salt, lemon and garlic, too, but that’s it. It’s hardly like you had to pick him out of a CROWD now, is it?”
Then I remind myself that I eat more spiced food than they do, and that I find it difficult to recognise ingredients from a cuisine that I’m not familiar with. It’s most definitely a learned thing.
Mon did that on “Friends” when she was trying to figure out Pheobe’s grandmother’s cookie recipie. Course, turned out the cookies were Nestle Tolhouse, muhahaha…Sorry, get back to your regular scheduled conversation.