Prepare the chicken filling:
Heat olive oil in a large skillet over medium heat. Add the chopped onion and sauté for 2-3 minutes until softened. Toss in the diced red and green bell peppers and cook for another 2 minutes. Stir in the minced garlic and sauté for 30 seconds until fragrant.

Season the filling:
Add the shredded chicken to the skillet, followed by the chili powder, cumin, smoked paprika, salt, and black pepper. Stir to coat the chicken in the spices. Pour in the salsa and cook for 2-3 minutes, allowing the mixture to heat through and slightly thicken. Remove from heat and stir in the cilantro, if desired.

Assemble the quesadillas:
Lay a flour tortilla flat on a clean surface. Sprinkle 1/4 cup of shredded cheese over half of the tortilla. Spoon a generous portion of the chicken filling over the cheese, then top with another 1/4 cup of cheese. Fold the tortilla in half to form a half-moon shape. Repeat with the remaining tortillas and filling.

Cook the quesadillas:
Heat a large skillet or griddle over medium heat. Lightly grease the surface with butter or cooking spray. Place one folded quesadilla onto the skillet and cook for 2-3 minutes on one side until golden brown and crispy. Flip carefully with a spatula and cook for another 2-3 minutes on the other side. Remove and repeat with the remaining quesadillas.

Serve and enjoy:
Cut each quesadilla into thirds or quarters and serve immediately with sour cream, guacamole, salsa, and lime wedges on the side.