1. Combine honey and lime juice in a small bowl, stirring well with a whisk. Stir sour cream into honey mixture; cover and chill until ready to serve.
2. Place tortillas flat on a work surface. Sprinkle 3 tablespoons cheese over half of each tortilla; top each tortilla with 1/4 cup chicken, 1/4 cup peaches, and 1 teaspoon cilantro. Fold tortillas in half.
3. Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Place 2 quesadillas in the pan, and top quesadillas with a cast-iron or other heavy skillet. Cook 1 1/2 minutes on each side or until tortillas are crisp and lightly browned (leave cast-iron skillet on quesadillas as they cook). Remove quesadillas from pan; set aside, and keep warm. Repeat procedure with the remaining quesadillas. Cut each quesadilla into wedges. Serve with sauce.