Preheat oven as required for baking.

Prepare the roux by melting the unsalted butter in a saucepan over medium heat, then whisk in the flour until smooth.

Gradually add the whole milk to the roux, stirring continuously until the mixture thickens.

Remove from heat and stir in the mozzarella cheese, sharp cheddar cheese, paprika, salt, and black pepper until the cheeses melt and the mixture is well combined.

Chop the cabbage and blanch it if desired before layering it in a baking dish.

Pour the cheese sauce over the cabbage, ensuring it is evenly coated.

Bake in the preheated oven for the specified cook time until bubbly and golden on top.