Cook the pasta in a large pot of salted boiling water until al dente, following the package instructions.
Drain and rinse the cooked pasta, then set it aside.
In a small bowl, beat one egg until smooth.
Set the egg aside.
Melt the butter in a large pot over medium heat.
Sprinkle in the flour and whisk together to create a roux.
Continuously whisk for about 5 minutes until the mixture turns a golden color.
Slowly pour in the milk while whisking constantly.
Add the dry mustard and continue whisking until the mixture thickens, about 5 minutes.
Reduce the heat to low and take a small amount of the sauce.
Add it to the beaten egg to temper it, then add the egg mixture to the pot.
Add in the grated cheese, salt, and black pepper.
Stir until the cheese is completely melted and the sauce is smooth.
Add the cooked macaroni to the sauce and stir to combine thoroughly.
Serve hot.