Add the zucchini, carrot, onion, bell pepper and mushrooms to a food processer. Pulse until mixture is finely chopped or minced.
Place mixture in a medium bowl with the remaining ingredients (except oil) and mix well. If mix is too loose, add a bit of bread crumbs. If it's too dry, moisten with a bit more egg or water. Form mixture into four patties. Cover and refrigerate for 30 minutes.
Heat the oil in a heavy skillet over medium heat. Add the four patties and cook burgers, turning carefully, until nicely browned (about 4-8 minutes per side).
Serve on buns with your choice of toppings.