In a medium bowl, combine shredded chicken, bell pepper, red onion, chili powder, and cumin. Mix well to combine.
Heat 1/2 tablespoon oil in a large skillet over medium heat. Place one tortilla in the skillet and sprinkle with 1/4 cup cheese.
Add about 1/2 cup of the chicken mixture over half of the tortilla, then top with another 1/4 cup cheese. Fold the tortilla in half to create a half-moon shape.
Cook for 3-4 minutes on each side until golden brown and cheese is melted. Transfer to a cutting board and repeat with remaining tortillas and filling, adding more oil to the skillet as needed.
Let quesadillas rest for 1 minute, then cut each into 3 wedges. Serve immediately with sour cream, salsa, and guacamole.