Heat a large heavy-duty skillet over medium-high heat.
Season both sides of the chicken breasts with kosher salt and freshly ground black pepper.
Add 1 tablespoon of olive oil to the hot pan, then add the chicken and cook 5–6 minutes per side, until cooked through; remove and let rest.
Return the pan to medium heat and add the remaining 1 teaspoon tablespoon of oil, then add the chopped onion, diced bell peppers, and garlic; cook 2–3 minutes until softened.
Add the diced tomatoes and fajita or taco seasoning, and cook another 2 minutes until the tomatoes soften and the mixture is combined.
Dice the rested chicken and return it to the pan; stir to combine and heat through.
Wipe the pan clean if needed and heat over medium. Add 1 teaspoon oil to the pan and place two tortillas in the pan.
Spread 1 teaspoon sour cream on one half of each tortilla, then layer with about half the cheese, avocado, and the chicken mixture; squeeze a little lime juice and sprinkle cilantro if using.
Fold the tortillas in half to form half-moons and cook 2–3 minutes per side, until golden brown and the cheese melts; repeat with remaining tortillas to make two more quesadillas.
Cut each quesadilla into wedges and serve immediately with extra lime wedges, sour cream, salsa, or guacamole if desired.
