Prepare fundido sauce by adding all sauce ingredients to food processor or blender and mix until smooth. Taste and add additional salt and pepper if needed. Set aside (or make in advance and refrigerate).
Mix chicken, salsa, cumin, oregano and 1 cup of cheese. 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.
Add enough oil to a skillet to just cover the bottom of the pan. Heat to medium. Once the oil is hot, pan fry the burritos, turning every 30 seconds or so, until golden on all sides. Place on a paper towel lined baking sheet.
Once all burritos are crispy, turn oven to high broil. Remove paper towel from under the burritos and spoon some fundido sauce over each burrito. Sprinkle with remaining cheddar cheese.
Broil for 2-3 minutes until warm and melty. Serve garnished with green onion.
To bake instead of pan fry, line burritos on a baking sheet, seem side down, and brush the tops lightly with olive oil or cooking spray. Bake at 400°F for 15-20 minutes or until golden brown and crispy.
Make ahead Instructions: The sauce can be made a week in advance, stored in the fridge. The chicken filling or the assembled burritos can be stored in the fridge for 2-3 days, depending on the freshness of ingredients. Freezing Instructions: Assemble the burritos and before pan-frying or baking, place them in a freezer safe bag or container and freeze for 3-6 months. Thaw overnight in the refrigerator, then continue with the pan-frying or baking steps of the recipe. For best results in flavor and texture I don't suggest freezing the sauce.