In a large bowl, combine the cooked brown rice, black beans, corn, chili powder, cumin, salt, and pepper. Mix well until all ingredients are evenly combined.
Heat a non-stick skillet over medium heat and add the olive oil.
Place a tortilla in the skillet and sprinkle 1/4 cup of shredded cheese on one half of the tortilla.
Spoon about 1/2 cup of the bean and rice mixture over the cheese, then fold the other half of the tortilla over to create a half-moon shape.
Cook for about 3-4 minutes on each side, or until the tortilla is golden brown and crispy, and the cheese is melted.
Repeat with the remaining tortillas and filling.
Serve the wraps warm, topped with avocado slices, shredded lettuce, and salsa.