Step 1

Make the coleslaw: In a medium bowl, stir together the cabbage, 2 tablespoons mayonnaise, apple cider vinegar, sugar, and caraway seeds. Set aside.

Step 2

In a small bowl, stir together the remaining ½ cup mayonnaise and Dijon mustard.

Step 3

Preheat a griddle or two large skillets over medium heat.

Step 4

Place the tortillas on the griddle or skillet. Place ¼ cup of cheese on half of each tortilla. (You may need to do this in batches, depending on the size of your griddle.)

Step 5

Top with ¼ of the corned beef and ¼ of the coleslaw per tortilla.

Step 6

Top with the remaining cheese, dividing it evenly among the tortillas.

Step 7

Fold each tortilla over to make a half moon. Cook until the underside is lightly browned, about 2 minutes.

Step 8

Flip and continue cooking until the bottom is lightly browned and the cheese is melted, about 2 minutes more.

Step 9

Remove from the griddle and cut the quesadillas as desired. Serve with the Dijon/mayo dipping sauce.