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, approximately 3 minutes. Add minced garlic and continue cooking for 1 minute until fragrant.
03 - Sprinkle flour into the skillet, stirring constantly for 1 minute to cook out raw flavor. Gradually whisk in whole milk and heavy cream, continuing to whisk until sauce thickens and bubbles form, about 3-4 minutes.
04 - Remove skillet from heat. Stir in salt, black pepper, and paprika. Add 1 cup mozzarella cheese and 1/2 cup parmesan cheese, stirring until completely melted and smooth.
05 - In a large mixing bowl, combine shredded cabbage, chopped corned beef, and prepared cheese sauce. Mix thoroughly until cabbage is evenly coated.
06 - Transfer mixture to the prepared baking dish, spreading evenly. Top with remaining 1/2 cup mozzarella cheese and additional parmesan to taste.
07 - Cover baking dish tightly with aluminum foil. Bake for 25 minutes to allow vegetables to steam and flavors to meld.
08 - Remove foil and return to oven for 15 minutes until cheese is golden brown and bubbly. Internal temperature should reach 165°F.
09 - Let casserole rest for 5-10 minutes before serving to allow setting. Garnish with fresh chopped parsley if desired.