Heat your oven to 325°F and grease a 9x13 inch baking dish.
Bring a large pot of salted water to boil; add the pasta and cook until just shy of al dente by about one minute. Drain and toss with a bit of olive oil to prevent sticking.
While the pasta cooks, shred all the cheeses and split them into three portions: about 3 cups for the sauce, and two 1 1/2 cup portions for layering.
In a saucepan over medium heat, melt the butter, then whisk in the flour until the mixture looks like damp sand; cook while whisking for one minute.
Gradually add about 2 cups of the half and half, whisking continuously until smooth, then pour in the remaining half and half plus the whole milk, stirring well to combine.
Keep whisking over medium heat until the sauce thickens substantially, resembling slightly thinned condensed soup.
Remove from heat and mix in the salt, pepper, paprika, and 1 1/2 cups of shredded cheese, stirring until melted and smooth. Add another 1 1/2 cups of cheese and stir again until fully incorporated.
Combine the drained pasta with the cheese sauce until evenly coated.
Pour half of the cheesy pasta into your prepared baking dish, sprinkle with 1 1/2 cups of shredded cheese, and then layer with the remaining pasta mixture.
Top everything with the final 1 1/2 cups of cheese and bake in the oven for about 15 minutes until the cheese is bubbly and just starting to turn golden.
Remove from oven and let it sit briefly before serving to allow the dish to settle.
