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. Cook for 1 minute, stirring constantly, to remove the raw flour taste.
04 - Gradually whisk in whole milk and heavy cream, ensuring no lumps form. Continue whisking until sauce thickens, about 3-4 minutes. Add salt, black pepper, and paprika. Remove from heat and stir in 1 cup mozzarella and 1/2 cup parmesan until melted and smooth.
05 - In a large mixing bowl, combine shredded cabbage, chopped corned beef, and prepared cheese sauce. Mix thoroughly until all components are evenly coated.
06 - Transfer mixture to the prepared baking dish, spreading evenly. Top with remaining 1/2 cup mozzarella and a generous sprinkle of additional parmesan cheese.
07 - Cover baking dish with aluminum foil. Bake for 25 minutes to allow vegetables to cook through and flavors to meld.
08 - Remove foil and continue baking for 15 minutes until cheese is bubbling and golden brown on top.
09 - Let casserole rest for 5-10 minutes before serving to allow flavors to settle. Garnish with chopped fresh parsley if desired.