Preheat oven to 400°F. Line a baking sheet with foil or parchment paper.
Make the filling: Mix chicken, salsa, cumin, oregano, cheese and onions. Place a heaping 1/2 cup or so of the chicken mixture in the center of each tortilla.
Fold the sides of the tortilla in and roll up tightly like a burrito. Place seam-side down on baking sheet. Brush lightly with olive oil or spray with non stick cooking spray.
Bake at 400°F for about 20-25 minutes or until golden brown and crispy.
Make the sauce: Meanwhile, prepare sauce by melting butter in a medium saucepan over medium heat. Once melted and bubbling, whisk in flour and cook, stirring constantly for about 3 minutes. Add minced garlic and stir for 30 seconds. Gradually whisk in chicken broth. Add cumin, oregano, and a dash of salt and pepper and cook, stirring, until thickened, about 2-3 minutes. Remove from heat and stir in green chilies, cheese and sour cream. Tastes and add more seasonings if needed.
Broil: Remove burritos from oven and turn the oven to HIGH broil. Ladle a spoonful of sauce over each burrito and top with a handful of shredded cheddar cheese. Broil for 2-3 minutes, or until cheese has melted.
Tortillas: I prefer to use uncooked flour tortillas, but regular flour tortillas work as well. Make ahead Instructions: The chicken filling and green chile sauce can both be made a day or two in advanced, making dinner prep super easy! Store them separately, covered in the fridge. Freezing Instructions: Make the burrito filling as instructed and roll up in tortillas (either uncooked or regular tortillas). Place in a freezer ziplock bag. Make the sauce but do not add the sour cream. Freeze sauce in a separate container. To bake from frozen place frozen burritos on a lined baking sheet, cover with tinfoil and bake at 350 degrees for 40 minutes. Uncover and bake for an additional 15-20 minutes or until warmed through and crisp on the outside. Add frozen sauce to a saucepan and warm. Stir in sour cream. Serve over cooked burritos.