Heat the olive oil. Saute the onion, garlic, tomatoes, chili and bell pepper with a bit of salt and black pepper for a minute or two.
Add the mushrooms. Sprinkle with more salt and black pepper. Continue sautéing until the mushrooms are half-cooked.
Add the beans and olives. Season with more salt and black pepper. Cook, tossing often, until the beans are heated through and the mushrooms are cooked. Turn off the heat.
Drizzle in the lime or lemon juice. Taste. Add more salt and black pepper, if needed.
Heat the tortillas (in a pan or on the grill) and start making the burritos.
Lay a tortilla flat. Arrange some greens in the middle. Top with heaping tablespoonfuls of the bean and mushroom filling. Smother with grated cheese then roll to seal. Repeat until all the tortillas are filled.
Serve the vegetarian burritos immediately.