Cook the peppers and onions: In a large skillet over medium-high heat, add 1 tablespoon olive oil, sliced peppers, and onions. Cook until peppers and onions start to caramelize in places, 8-10 minutes. Scoop out onto a plate and set aside.
Make the chicken and bean filling: In the same skillet over medium heat, add 1 tablespoon olive oil, the shredded chicken, and beans. Stir together until warm. Add the salt, chili powder, and cumin, and then add the salsa verde. Remove from heat.
Assemble the burritos: Wrap one 12-inch tortilla or four 8-inch burritos in a few paper towels. Microwave on high for 15 seconds to make the tortillas warm and flexible.
Then, in the lower-middle section of the tortilla, add 1/3 cup cilantro rice, 1/3 cup peppers and onions, 1/2 cup of the chicken and bean mixture, and 1/4 cup grated cheese. (If you’re using smaller 8-inch tortillas, divide these amounts evenly among the four tortillas). Tightly roll the tortilla, folding over the ends, to form a burrito. Once formed, wrap the burrito in heavy-duty aluminum foil.
