Slice pepper and onion into strips (cut onion lengthwise). Chop cilantro and set aside. Prepare guacamole and sour cream, if needed.
Heat 1 tablespoon olive oil in a skillet (I prefer cast iron for this recipe) on medium-high heat.
Add the pepper and onion to the pan and cook for a few minutes, stirring often, until they're tender-crisp.
Add in the chicken, spices, salt & pepper, and lime juice. Stir and set aside (off the heat).
In another skillet, heat 1 teaspoon of olive oil on medium heat. Once the skillet is hot, place one tortilla inside. Sprinkle it with half the cheese, the fajita mixture from the other skillet, chopped cilantro, and then the rest of the cheese. Place the second tortilla on top and push it down carefully.
Flip the quesadilla using a spatula once the bottom tortilla begins to brown (about 2-3 minutes). Cook the other side for another 2-3 minutes or until cooked to your liking. Both sides should be browned and the cheese should be melted.
Place quesadilla on a plate and cut into quarters. Serve immediately with sour cream and guacamole.