Prepare the vegetables. Dice the onion into small, even cubes. Dice the red and green bell peppers into small pieces so they cook quickly and fit neatly inside the tortillas.
Season the chicken. Add the cooked chicken to a mixing bowl. Sprinkle in chili powder, cumin, garlic powder, smoked paprika, salt, and black pepper. Toss until the chicken is evenly coated and smells warm and savory.
Cook the vegetables. Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the onion and bell peppers. Cook for 4 to 5 minutes, stirring often, until the onion looks slightly translucent and the peppers are tender.
Assemble the quesadillas. Spread shredded cheese evenly on half of each tortilla. Layer seasoned chicken and sautéed vegetables over the cheese. Fold tortillas in half.
Cook the quesadillas. Heat a skillet over medium heat. Add melted butter or oil. Cook each quesadilla for 2–3 minutes per side until golden and crisp. Use a spatula to press gently for even browning.
Serve. Slice into wedges. Serve with sour cream, salsa, lime wedges, and optional cilantro.