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© Meredith Corporation. All rights reserved. Used with permission.
Place each chicken breast half between two pieces of plastic wrap. Using the flat side of a meat mallet, pound chicken lightly to about 1/2 inch thick. Discard plastic wrap. Stir together cumin, salt, black pepper and cayenne in a small bowl. Sprinkle mixture evenly over chicken; rub in with your fingers.
Grill chile peppers on the rack of an uncovered charcoal grill, directly over medium coals, for about 15 minutes or until peppers are charred on all sides, turning occasionally. Immediately wrap peppers in foil; set aside. Place chicken on grill rack directly over heat. Grill for 8 to 11 minutes or until chicken is no longer pink (170°F), turning once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Place chile peppers, then chicken, on grill rack over heat. Cover and grill as directed.)
Cut chile peppers in half lengthwise; remove stems and seeds. Using a sharp knife, gently peel off skins and discard. Cut peppers into 1-inch strips. Cut chicken into 1-inch pieces.
In a large bowl, combine chile peppers, chicken, Cheddar cheese and Monterey Jack cheese. Place some of the chicken mixture on half of each tortilla. Fold tortilla in half and press together firmly. Grill quesadillas directly over medium heat for about 4 minutes or until heated through and light brown, turning once halfway through grilling. To serve, cut quesadillas in half.