Start by making the Mexican shredded chicken (if you haven’t already). Combine boneless chicken, salsa, green chilies, and spices in your slow cooker. Cook until the chicken is tender, then shred it thoroughly.
Preheat the oven to 400°F (200°C). Line a baking sheet with foil, and place a wire rack over it. Lightly coat the rack with nonstick spray.
Lay a large tortilla flat, spoon about a half cup of shredded chicken in the center, and sprinkle cheese on top. Roll it tightly, tucking the ends in as you roll. Place the burrito seam-side down on the wire rack.
Lightly brush olive oil over all sides of the burritos. This ensures a crispy, golden exterior.
While your burritos bake, prepare the sauce. Start by melting butter in a saucepan with olive oil. Whisk in the flour and cook for 2–3 minutes. Gradually add warm chicken broth, stirring constantly. Bring the mixture to a simmer until thickened. Finally, stir in green chilies, cheddar cheese, and sour cream. Add hot sauce if desired.
Place the burritos in the oven and bake for 18–20 minutes. For extra crispness, broil them for an additional 2 minutes per side.
Drizzle the creamy green chili sauce generously over the baked burritos, and garnish with your favorite toppings like fresh cilantro, diced tomatoes, and avocado.