I love having variety in my food so it's really hard to decide. I would say that my favorite foods come from the Mediterranean, Central America, and Southeast Asia, so basically I'm cheating. Those aren't unique countries/cultures.
Let's challenge me to be ultra-specific to three for the rest of my life.
1) Italy - pizza, pasta, olives, salads, wine ...Italy was probably my first favorite as a child which is likely why it's still kind of an ultimate comfort food for me from veggie pizza to black olives to red wine. When I was really little the very first fancy restaurant I went to with my grandparents was a family owned Italian place. I always got the cheese lasagna in a deep dish with a Shirley Temple. Then by middle school my favorite food was pizza. I also lived with an Italian-Argentine family for a while and dated the son, which just reinforced my childhood prejudices for tomato sauces and high carbs in food, while building on the wine front, and adding green chimichurri and veggie empanadas.
2) Lebanon - while living in LA I realized I really, really loved Lebanese food...their specific versions of falafel, hummus, tahini sesame paste (it's the sesame!), baba ganoush, pita, rice, tabbouleh, and of course, Lebanese pickles. I used to go to this one place and get falafel wrapped in a pita with salad topping, extra extra tahini sauce, and extra extra pink Lebanese pickled turnips. There's a fancier place I enjoyed too which was very nice, the people were kind and generous, but the place where I could get the pita wrap is literally the last place I went out to eat in Los Angeles before I moved. Lebanese people also put really awesome flavors into their ice cream like rose water, lavender, green tea, and orange oil. I was introduced to it as well while working near Wilshire and Westwood as a vegetarian, and these unique full-bodied flavors translate well to vegan nice creams. Nothing made me love Arabic culture more than working in Little Armenia, and I know this (and not public shaming) is the key to anti-racism.
3) South India - South India has more vegetarians than North India, and has a very specific Indian cuisine that makes me happy. Thali plates are really fun to eat in a restaurant, and dosas are like Asian burritos. At home I now make curry a bunch with potatoes, peas, onions and coconut milk (as well as spices, and possibly other add-ins) because it's a cheap, delicious meal, and have discovered the joy of chutneys, for everything from their intended purpose (Indian food) to pita chips to baked potatoes. I also like that lentils are so popular in India because sometimes I find them easier to take than beans, they have a milder flavor and texture. It's pretty easy to veganize Indian food and canned, full-fat coconut milk is indispensable for various reasons.
Honorable mentions to Japan and Mexico. I know. I'm cheating.