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