Prepare Mexican Chicken according to the linked recipe; drain excess liquid.
Preheat oven to 400°F. Line a baking sheet with foil and place a rack on top.
Assemble burritos with ½ cup chicken filling each, cheese, and roll up. Place on the rack.
Brush or spray burritos with oil and bake for 18-20 minutes until golden. Broil for crispiness.
For the sauce, heat oil and butter, whisk in flour, then slowly add chicken broth. Add spices and simmer until thick. Off heat, add chilies, cheese, and sour cream. Season with hot sauce.
Serve burritos topped with sauce and optional toppings.
