Prepare pasta according to the package directions. Make the sauce while the pasta is cooking.
Make a basic white sauce by melting the 3 tablespoons of butter, add the flour, and cook over medium heat for about 1 minute. Then slowly add in the cold milk, and stir the sauce until it is thickened.
Add the white American cheese into the white sauce. If the white American cheese is not sliced, cut it into cubes. In a medium-sized pot add the American cheese and as it begins to melt, slowly stir in the milk.
Once the American cheese has fully melted, begin to stir in the white sharp cheese. Stir in the Dijon mustard. The cheese sauce should be ready the same time the pasta is done. Combine the cheese and the pasta together. Serve immediately.