Preheat the oven broiler with a rack in the bottom half of the oven.

In a medium saucepan, heat the milk until just under a gentle boil. Remove from the heat and stir in the butter to melt it.

Whisk the egg yolks in a small bowl, then temper them by slowly drizzling in about 3 large spoons of the hot milk mixture, whisking constantly.

Pour the tempered eggs into the saucepan, whisking constantly.

In a blender or food processor, combine 3 cups of the cheddar, the grated mozzarella, Parmesan, and quartered American cheese slices.

Sprinkle in the paprika, salt, and pepper.

Pour the hot milk mixture into the blender and blend it on high for 30 seconds, until all the cheese is melted and the sauce is totally smooth. It should be pretty thin and pourable, but still have a nice silkiness.

Pour the macaroni into a large bowl, pour all the sauce on top, and stir to mix.

The pasta should be very saucy; splash in a little pasta water as needed. Taste a spoonful of the mac and cheese and add more salt and pepper to taste!

Butter a 9 x 13-inch baking dish and add half of the saucy macaroni.

Add half of the remaining cheddar and half of the diced mozzarella.

Pour in the rest of the macaroni, and top with the rest of the cheddar and diced mozzarella.

Broil until the cheese is bubbling and starting to turn brown, about 10 to 12 minutes, watching to make sure it doesn't burn. Serve immediately while it's hot and saucy!