Bring a large pot of salted water to a boil and cook the pasta for 1 minute less than the package directions recommend.
Blend the cottage cheese, milk, cornstarch, Dijon mustard, garlic powder, smoked paprika, and black pepper until completely smooth.
Drain the pasta, reserving 1/2 cup of the cooking water, and return the pasta to the warm pot.
Pour the blended cottage cheese sauce into a saucepan and warm it over medium-low heat for 3 to 4 minutes, stirring constantly.
Add the cheddar, Monterey Jack, and Parmesan to the sauce a handful at a time, stirring until melted and glossy.
Pour the cheese sauce over the pasta and stir until every piece is coated, adding a splash of reserved pasta water if needed.
Rest the mac and cheese for 3 minutes before serving so the sauce thickens.