Heat olive oil in a large skillet, over medium heat. Sauté onions and garlic until onions are translucent, season with salt and pepper. Add shredded carrots, cumin, coriander, chili powder, and cayenne pepper, cook until carrots are tender. Remove pan from heat.
In a large bowl, mash the beans. Add the contents of the pan along with the soy sauce, egg and quick oats. Thoroughly mix everything together, then form into 4 large or 6 small patties. Place the patties in freezer for 30 minutes to set.
Cook patties in a large skillet, coated with non-stick cooking spray over medium heat. Flip once the patty is brown and crisp, repeat on other side until cooked through. Serve immediately on toasted buns with lettuce, tomato, avocado and onions.