01 - Preheat oven to 375°F. Grease a 9x13-inch baking dish with butter or cooking spray.
02 - Melt butter in a large skillet over medium heat. Add diced onion and cook until softened, about 3 minutes. Add minced garlic and cook for 1 additional minute until fragrant.
03 - Stir flour into the butter and onion mixture, cooking for 1 minute to remove raw flour taste. Gradually whisk in whole milk and heavy cream, continuously whisking to prevent lumps. Continue whisking until sauce thickens, approximately 3–4 minutes.
04 - Stir in salt, black pepper, and paprika. Remove skillet from heat. Add 1 cup mozzarella cheese and 1/2 cup parmesan cheese, stirring until completely melted and sauce is smooth.
05 - In a large mixing bowl, combine shredded cabbage, chopped corned beef, and prepared cheese sauce. Mix thoroughly until cabbage is evenly coated with sauce.
06 - Spread cabbage and beef mixture evenly into the prepared baking dish. Top with remaining 1/2 cup mozzarella cheese and a generous sprinkle of additional parmesan cheese.
07 - Cover baking dish with aluminum foil. Bake for 25 minutes to allow vegetables to steam and flavors to meld.
08 - Remove foil and continue baking for 15 minutes until cheese is bubbly and golden brown on top.
09 - Let casserole rest for 5–10 minutes before serving to allow set. Garnish with chopped fresh parsley if desired.