The full-send baked version: a three-cheese béchamel under a brown-butter, garlic-Parmesan breadcrumb crust. Consider this the reward.
Heat the oven to 375F. Boil the cavatappi in well-salted water 2 minutes short of the package time so it stays toothsome under the bake. Drain and set aside.
Make the crust first so the pan's free: melt the 3 tbsp butter over medium heat and let it foam, then keep going until the milk solids turn golden and it smells nutty. Stir in the panko and garlic, toast 2 minutes until golden, then off the heat fold in the Parmesan. Tip it into a bowl.
In the same pot, melt the 5 tbsp butter, whisk in the flour, and cook 2 minutes to a pale roux. Pour in the warm milk in a slow stream, whisking constantly so it stays smooth, then add the cream. Simmer, whisking, until it thickens enough to coat the back of a spoon, about 5 minutes.
Drop the heat to low. Whisk in the Dijon, paprika, and nutmeg, then add the cheeses in handfuls, stirring until each melts before the next. Add the cheese off a hard boil and over low heat; if the sauce gets too hot it breaks and turns grainy. Season with salt and pepper.
Fold the drained pasta into the sauce until every piece is coated, then pour into a buttered baking dish. Blanket the top evenly with the brown-butter breadcrumbs.
Bake 20 to 25 minutes until bubbling at the edges and deeply golden on top. Let it sit 5 minutes before serving so the sauce sets enough to scoop.