Slice the chicken breasts into strips, about an inch apart, and coat with taco seasoning. In a large skillet, heat 1 Tbsp. vegetable oil and cook chicken until no longer pink and slightly charred. Remove cooked chicken from the skillet.
Heat another Tbsp. oil, add onion and garlic and cook for a couple minutes until it’s slightly translucent. Add the peppers, and cook slightly, then mix in the cooked chicken. Remove from heat and set aside.
In a clean pan, melt a bit of butter. Add a tortilla and move it around until it’s buttery. Add cheese, then fajita mixture, then more cheese, then top with another tortilla and pat it down.
Flip the quesadilla over and cook the other side until it’s golden. Remove from pan and cut into quarters. Repeat these steps with the remaining tortillas.