Prepare the pasta al-dente (soft but slightly firm) according to the package instructions in a large pot of boiling salted water.
While the pasta is cooking, blend the egg yolks, half and half, salt, pepper, and yellow mustard on a medium-high speed for 5 seconds. With the lid removed, turn the blender on the lowest speed. In a steady thin stream, slowly pour the butter into the blender. Once all the butter has been added, turn the blender off. If you don't have a blender, you can whisk the ingredients by hand.
After the pasta is done cooking, quickly drain the pasta and return it to the pan reducing the heat to the lowest setting.
Stir in the sauce followed by the cheese. Continue to the stir the pasta until the cheese has melted and the pasta is creamy and cheesy.
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