In a large skillet, heat 2 tablespoons of the olive oil over medium heat. Add the chicken in a single layer. Season with salt and cook until browned all over, about 6 minutes. Add the bell peppers and onions and cook, stirring often, until peppers and onions have softened, about 4 minutes more.
Add the corn, onion powder, garlic powder, smoked paprika, cumin, oregano, and black pepper. Cook, stirring continuously, until everything is coated and corn is warmed through, about 2 minutes. Stir in the cilantro, if using, and transfer to a large bowl.
In a medium bowl, combine the Monterey Jack and cheddar cheese. On a clean work surface, top half of each tortilla with 3 tablespoons of cheese. Top with ½ cup chicken filling and spread out into an even layer. Top with 2 tablespoons of cheese and fold the tortilla over the filling.
Wipe out the skillet from the filling. Heat ½ tablespoon olive oil over medium-low heat. Once the oil is glistening, add two quesadillas at a time. Cook until golden brown and crispy, about 3 minutes per side. Transfer to a cutting board and repeat with the remaining quesadillas, adding ½ tablespoon oil as needed.
Cut the quesadillas into thirds and serve with the sour cream, guacamole, and pico de gallo if using.