Cook the pasta according to the package directions. Drain well.
While the pasta is cooking, melt 3 tablespoons of butter in a large pot over medium heat. Stir in the flour to create a thick paste. Then slowly add the cold milk and Dijon mustard, and whisk the ingredients until they're combined.
Next, add the white American cheese into the white sauce. If the white American cheese is not sliced, cut it into cubes first so that it melts easier.
Once the American cheese has fully melted, stir in the white sharp cheese and a dash of salt. The cheese sauce should be ready at the same time the pasta is finished cooking.
Stir the pasta into the cheese sauce, and serve hot.