Preheat your oven to 400°F. Line a baking sheet with foil or parchment paper; this will help with the cleanup later!
To make the filling, mix together the chicken, salsa, cumin, oregano, cheddar cheese, and green onions in a large bowl. You want everything well combined for maximum flavor.
Take a large flour tortilla and place a heaping ½ cup of the chicken mixture in the center. Be careful not to overfill, or you’ll have trouble rolling them up!
Fold the sides of the tortilla in and roll it tightly to form a burrito. Place the burrito seam-side down on the prepared baking sheet.
Brush the tops lightly with olive oil or spray with non-stick cooking spray. This will help them crisp up beautifully.
Bake the burritos in the preheated oven for about 20 to 25 minutes, or until they are golden brown and crispy. Keep an eye on them to avoid burning.
While the burritos are baking, prepare the sauce. Melt the butter in a medium saucepan over medium heat. Once it's melted and bubbling, whisk in the flour and cook, stirring constantly for about 3 minutes. This creates a roux.
Add the minced garlic and stir for 30 seconds, allowing the flavors to meld.
Gradually whisk in the chicken broth, stirring until the mixture is smooth.
Next, add the remaining cumin, oregano, and a dash of salt and pepper. Cook, stirring until thickened, about 2 to 3 minutes. Remove from heat and stir in the green chilies, cheddar cheese, and sour cream. Taste and adjust the seasonings as needed.
Once the burritos are done baking, remove them from the oven and set your oven to HIGH broil.
Ladle a spoonful of the sauce over each burrito and top with a handful of shredded cheddar cheese. Broil for 2 to 3 minutes, or until the cheese is melted and bubbly.
Serve your delicious Smothered Green Chile Chicken Burritos with authentic Mexican rice for a complete meal!
