Bring a pot of water to a boil, add the pasta, and cook (stirring often) for 20 minutes. Yes, 20 minutes. Drain well.
1 lb elbow noodles
Add the butter to a large sauce pan and set it over medium heat to melt. Once melted whisk the flour in to form a paste and let it cook for 60 seconds.
1/4 cup butter, 1/4 flour
Pour the milk in, one cup at a time, whisking until evenly combined each time. Add the paprika and whisk until the mixture's thickened, about 2-3 minutes.
2 cups whole milk, 1/8 tsp paprika
Transfer some of the roux to a small bowl, add the egg yolk and quickly whisk them together until evenly combined to temper the egg. Whisk the tempered egg mixture int the roux in the skillet.
1 egg yolk
Reduce the heat to low and add the american cheese pieces, half the cheddar cheese, and Italian cheese to the roux. Stir the mixture together until the cheese has melted completely and the sauce is smooth.
8 slices American cheese, 16 oz mild shredded cheddar, 1 cup shredded Italian blend cheese
Add the cooked and drained pasta to a 9x13" baking dish, pour the cheese sauce evenly out over top, and gently stir together until evenly combined. Spread out in an even layer in the dish.
Sprinkle the remaining cheddar cheese evenly out overtop, and broil (watching closely) until cheese is melted and golden brown on top.
Carefully remove the dish from the oven, let rest for 10 minutes, then serve warm & enjoy!