Follow the recipe instructions to prepare Mexican Chicken. (Click on 1 Recipe Slow Cooker Mexican Chicken recipe). You should drain any liquid left over from the chicken.
Pre-heat oven to 400°F. Line a baking tray with foil and place a baking rack on it. Make burritos: Add a generous 1/2 cup of filling to each tortilla (uncooked for raw tortillas), then top each burrito with the desired amount cheese. Place burritos on a baking rack. Brush both sides with olive oil or spray nonstick cooking spray. Cook burritos for 18-20 minutes, or until golden. Broil until desired crispiness is achieved. Flip the pan over and broil the opposite side until golden.
In the meantime, heat butter and olive oil in medium saucepan on medium heat. Mix in flour, and cook stirring continuously for 3 minutes. Reduce heat to low and then slowly whisk in the chicken broth. Stir in the spices. Bring to a boil, stirring occasionally until thickened. Stir in green chilies and cheese. Finally, remove from heat. Hot sauce may be added if desired.
Serve burritos with Cheesy Green Chili Sour Cream Sauce.