Preheat the oven to 350°F. Line two cookie sheets with parchment paper or spray them with olive oil spray. Place the chopped carrots into the bowl of a food processor fitted with a metal blade. Cover and process until finely minced and nearly pureed. Set aside.
Heat the oil in a large, deep sauté pan over low-medium heat. Add the garlic, onions, and string beans. Sprinkle with salt and pepper, the cumin, and the chipotle powder. Stir to coat. Cover and cook for 6 minutes, stirring frequently. Add the peppers, the yellow squash and zucchini, the corn, cilantro, and the minced carrots. Stir to combine. Cover and continue cooking for about 4 minutes, until the vegetables are crisp-tender, or cook a few minutes longer until they are cooked to your preference. Add the tomato and the drained beans. Stir to combine. Cover and cook for 2 minutes until heated through. Taste for seasonings.
Arrange 3 tortillas on each of the prepared cookie sheets. Divide the filling on the center of each tortilla, leaving 1inch on each end without filling. Sprinkle alittle of each cheese over the filling. Pull the sides of the tortillas in just to meet the filling. Take one side of the tortilla and cover the filling, then roll the tortilla until the seam side is down. Bake in the preheated oven for about 12-15 minutes until the tortillas are soft-crispy. Remove from the oven and arrange avocado slices, if desired, over each burrito.