Cook the cavatappi according to package directions; drain and set aside.
In a large saucepan, melt the butter over medium-high heat. Whisk in the flour until completely smooth.
Slowly whisk in the milk. Continue to cook, whisking occasionally, until the mixture is slightly thickened.
Add the cheese, a handful at a time, whisking well after each addition making sure the cheese is melted before adding more. Season to taste with salt and pepper. Remove from the heat.
Stir the cavatappi into the cheese sauce until all of the pasta is well-coated. Serve immediately.
