Preheat the oven to 350°F. Grease a 9x13-inch baking dish with 2 tablespoons of the butter.

In a heavy saucepan, whisk together the heavy cream, half-and-half, and remaining 4 tablespoons butter over medium-low heat. Add the black pepper, red pepper flakes, nutmeg, and ground mustard. Whisk in the flour and cook for about 2 minutes until smooth — the mixture should not bubble.

Reduce heat to low and whisk in the cheddar, manchego, and Gruyère cheeses until melted and smooth. Keep the sauce on low heat.

Bring 8 cups of water to a boil in a large stockpot. Add the salt and elbow macaroni. Cook for about 8 minutes until al dente — do not overcook. Drain and transfer to the prepared baking dish.

Pour the beaten eggs over the hot pasta and toss quickly to combine. Pour the cheese sauce over the macaroni and stir well to coat evenly. Sprinkle smoked paprika on top.

Bake for 40 minutes until the top forms a golden crust and the edges are bubbly. Let cool for 10 minutes before serving.