Korean Beef and Kimchi Quesadillas



5 tablespoons light brown sugar
3½ tablespoons soy sauce
1 teaspoon ginger (minced)
dash of red pepper flakes
2 teaspoons sesame oil
¾ pound lean ground beef
3 cloves garlic (minced)
3 extra large flour tortillas (10-inch)
1½ cup shredded mozzarella
¼ cup kimchi (cut into bite size pieces), plus more for serving
3 green onions (finely chopped)