Bring a large pot of salted water to a boil. Add the cabbage wedges and parboil for 1 to 3 minutes, just until slightly softened. Drain thoroughly, then carefully remove and discard the cores.

Preheat the oven to 350°F (175°C). Lightly grease a 9×9-inch baking dish with baking spray. Arrange the parboiled cabbage wedges evenly in the prepared dish and set aside.

In a nonstick skillet set over medium heat, melt the butter. Whisk in the flour and cook for 1 to 2 minutes, stirring continuously, until a smooth roux forms.

Gradually whisk in the milk in small batches, stirring constantly to prevent lumps, until the sauce thickens and becomes smooth.

Remove the skillet from the heat and stir in the mozzarella and sharp cheddar cheeses until fully melted and incorporated. Season the sauce with kosher salt and freshly cracked black pepper to taste.

Pour the cheese sauce evenly over the prepared cabbage. Sprinkle paprika lightly over the top for garnish.

Bake uncovered for 20 to 25 minutes, or until the casserole is bubbling and lightly golden on top.

Remove from the oven and allow the dish to rest briefly before serving. Serve warm.