*Jalapeño peppers can sting and irritate the skin, so wear rubber gloves when handling peppers and do not touch your eyes.
1. Heat oil in large skillet over medium-high heat. Add onion and jalapeño pepper; cook and stir 3 minutes or until onions are golden. Add cherries; cook and stir 1 minute. Stir in brown sugar, vinegar and salt. Cook over low heat 1 minute, stirring constantly. Remove from heat; cool slightly.
2. Arrange half of ham slices and half of cheese slices over one side of each tortilla. Top with one fourth of cherry jam. Fold tortillas in half. Remove and reserve any remaining jam.
3. Melt butter in skillet over medium heat. Add quesadillas; press down firmly with spatula. Cook 3 to 4 minutes per side or until golden and cheese melts. Remove from skillet. Cut each quesadilla in half. Serve with remaining cherry jam.