Combine ham, cheese, corn and chiles. Spoon heaping 1/2 cup filling on one half of each tortilla. Fold tortillas in half forming a half moon shape.
Melt 1/2 tablespoon butter in large skillet over medium heat. Place one filled tortilla in skillet and cook approximately 1 minute on each side, or until browned and crisp. Repeat with remaining filled tortillas.
Cut each quesadilla into wedges. If desired, serve topped with sweet onion mustard or salsa.