In a medium bowl, combine the shredded chicken, olive oil, chipotle sauce, honey, cumin, garlic powder, salt, and pepper. Mix thoroughly until the chicken is well coated with the sauce.
Heat a non-stick skillet over medium heat. Place one flour tortilla in the skillet.
On half of the tortilla, layer a generous amount of the chipotle honey chicken mixture, followed by a mix of cheddar and Monterey Jack cheeses.
Fold the tortilla over the filling and cook for about 3-4 minutes, or until the bottom is golden brown and the cheese starts to melt.
Carefully flip the quesadilla and cook for another 2-3 minutes until the other side is golden and crispy.
Remove from the skillet and let cool for a minute before slicing into wedges.
Repeat the process for the remaining tortillas and filling.
Serve the quesadillas warm, garnished with fresh cilantro, and alongside sour cream and salsa.