Heat oil in a large skillet over medium heat. Add the onions and peppers and cook for 15-20 minutes, stirring occasionally, until tender and caramelized.
Add the garlic and cook another 30-60 seconds. Stir in the shredded chicken and seasonings and remove from heat. (If making in advance, place filling in a container, cool off for 20 minutes and then place covered in fridge.)
Preheat a griddle or large skillet over med-low heat. Place tortilla on the griddle and sprinkle on ~1/3 cup cheese. Add a layer of chicken filling and then top with another ~1/3 cup cheese and another tortilla. Cook for about 3-4 minutes or until cheese is melted and tortilla is golden and crispy. Flip and cook 2-3 minutes until cheese is melted and bottom tortilla is golden.
Slice and serve with sour cream, guacamole, salsa, cilantro...