Step 1: Preheat your oven to 375°F (190°C). Lightly grease a baking dish large enough to comfortably hold your four burritos.
Step 2: In a large mixing bowl, combine the shredded chicken, cooked rice, black beans, shredded cheddar cheese, diced red bell pepper, diced green bell pepper, and diced red onion. Mix thoroughly until all ingredients are evenly distributed.
Step 3: Lay out your flour tortillas on a clean surface. Spoon an equal portion of the chicken mixture down the center of each tortilla. Fold the shorter sides of the tortilla inwards over the filling, then tightly roll up each tortilla from one long side to the other. Place the rolled burritos, seam-side down, into your prepared baking dish.
Step 4: In a medium saucepan, melt the unsalted butter over medium heat. Once the butter is fully melted, sprinkle in the all-purpose flour. Whisk constantly for 1-2 minutes to cook the flour and create a smooth roux.
Step 5: Gradually add the milk to the roux, whisking continuously to prevent lumps. Continue to whisk until the sauce is smooth and begins to thicken slightly.
Step 6: Stir in the diced green chilis, salt, black pepper, garlic powder, and onion powder. Allow the sauce to simmer gently for another 2-3 minutes, letting the flavors deepen and the sauce reach your desired consistency.
Step 7: Carefully pour the warm green chili sauce evenly over the assembled burritos in the baking dish, ensuring they are generously covered.
Step 8: Transfer the baking dish to your preheated oven. Bake for 20-25 minutes, or until the burritos are heated through, the sauce is bubbly, and any visible cheese is golden brown.
Step 9: Remove the burritos from the oven. Garnish generously with a dollop of sour cream, a sprinkle of fresh chopped cilantro, slices of creamy avocado, and a squeeze of fresh lime juice, if desired. Serve immediately and enjoy your delicious homemade meal!