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 soft, about 3 minutes. Add minced garlic and cook for 1 minute until fragrant.
03 - Stir flour into the skillet and cook for 1 minute. Gradually whisk in milk and heavy cream, whisking constantly 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 cheese and 1/2 cup parmesan cheese, stirring until completely melted and smooth.
05 - In a 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 cheese and a generous sprinkle of additional parmesan cheese.
07 - Cover baking dish with aluminum foil. Bake for 25 minutes until heated through.
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. Garnish with chopped fresh parsley if desired.