Way back, when I used to have a lot of friends and family I would get together with, sometimes I'd be doing all the cooking, but usually sharing the chores with friends. One dish Mom would ask for every birthday was a dish from the book From Julia Child's Kitchen - A Pork Ragout, which was cubes of pork shoulder rubbed with a dry marinade of salt, pepper, garlic, and fresh rosemary and sage (original recipe just had thyme, but left the possibility for ), pounded to a paste, and rubbed all over the meat, and I always let it marinate the maximum 3 dqys. It also had fresh tomatoes, but was also good with canned, and had mushrooms and white wine in it. And , of course, butter!! This also paired with a mix of half and half potatoes and rutabagas, mashed, and I always baked some bread to go with it. Paired veggies and desserts varied, but these were the ones I would be asked for every time.
When getting together for Chinese dinners with some friends, that Szechwan eggplant dish and the 1,2,3,4,5 spareribs were things I was always asked to cook. Earlier on, I would make a non-hot dish, and a hot one, since several people didn't like the heat, but eventually, they all started liking the heat.
And something else that I am almost always expected to have, for some leftover sandwich makings, is the various sour rye breads I bake.
And for holiday dinners, I had a cauliflower au gratin I made one time, and my uncle, who hated cauliflower from childhood, loved this, and insisted it couldn't be cauliflower, and made up some name for it! And I always brought one batch of brownies, and various pumpkin pies, one way back in the 90s (maybe 80s?), a Cognac Pumpkin pie, from a cover recipe from a Gourmet Magazine. Later one from a bon apétit magazine - a true butterscotch pumpkin pie. These things aren't really my "signature" recipes, just things I was always expected to cook for those dinners.
In the summer there are a couple of what you might call signature dishes, such as that gazpacho, and the raw tomato pasta sauce, that varies greatly, but always has some fresh tomatoes, garlic, olive oil, and basil. Things people are always checking out my fridge for in the summer , to see if I have any.