In a large bowl, combine the shredded chicken, minced chipotle, cumin, smoked paprika, salt, and pepper. Mix well to ensure the chicken is well coated in the spices.
Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the sliced red onion and bell pepper. Sauté for 5-7 minutes, or until the vegetables are tender and slightly caramelized. Remove from heat and set aside.
In the same skillet, add another tablespoon of olive oil and place one flour tortilla in the pan. On one half of the tortilla, layer a generous amount of the chicken mixture, followed by a mix of the cheddar and Monterey Jack cheese. Add sautéed vegetables on top.
Fold the tortilla over to create a half-moon shape. Cook for about 3-4 minutes on each side, or until the tortilla is golden brown and the cheese has melted. Remove from the skillet and place on a cutting board.
Repeat the process with the remaining tortillas and filling.
Once all quesadillas are cooked, slice them into wedges and arrange them on a serving platter.
Garnish with fresh cilantro and serve with lime wedges on the side for an added burst of flavor.