Start the water for the pasta and turn the oven to broil. Eventually, when the pot comes to a boil, add salt, let it come to boil again, and cook the pasta to al dente.
1 pound cavatappi
Meanwhile, cut up the cheese into cubes and blitz in the food processor.
8 ounces sharp cheddar or other cheddar cheese, 3 ounces Parmesan, 5 ounces gruyere or other Swiss cheese
Make the cheese sauce. In a medium size saucepan, melt the butter over medium-low heat, then add the flour, whisking constantly to make a roux.
4 tablespoons butter, ¼ cup all purpose flour
Slowly pour in the milk and cream, whisking constantly, until the sauce is thickened until it coats the back of a spoon.
1 cup milk, 1 cup cream
Add in about two thirds of the cheese, reserving enough to top your pan. Then add the paprika, salt and pepper. Taste and then adjust the salt and pepper as needed.
½ teaspoon smoked paprika, ¼ teaspoon salt, ⅙ teaspoon black pepper
When the pasta has finished cooking, drain the pasta and return it to the pasta pot. Add the cheese sauce to the pasta and then mix them together in the pasta pot.
Pour the mixture into a 9 inch by 13 inch glass pyrex or other baking pan or casserole dish. Top with remaining cheese and slide the pan under the broiler until browned to desired brownness, about 5 to 10 minutes, watching it carefully so it does not burn.