Spread 2 tablespoons dressing on one side of each tortilla. Layer one-fourth corned beef, 1/2 cup sauerkraut, and 2 cheese slices evenly onto half of each tortilla. Fold tortillas in half over filling, pressing gently to seal.
Heat a large nonstick skillet coated with cooking spray over medium heat. Add quesadillas, in batches, and cook 2 to 3 minutes on each side or until golden brown and cheese is melted. Cut quesadillas into wedges, and serve immediately.