If you go to an upscale establishment with price tags to match, ask if the chef will make you a vegan meal. After all, while they may not offer a set vegan entree, there are usually lots of veggies and grains being used throughout the menu. Chefs at restaurants like these may appreciate the challenge and be willing to make you your own personal creation.
I did this at the Olde Pink House and was easily accommodated, with my only additional parameter being no olives (they just aren’t for me). I don’t know how well this would work at a more casual restaurant, but you could always ask and see what happens. I’m sure it depends on who’s in the kitchen.