Cook the pasta according to package directions. Reserve ¼ cup of pasta water, drain it, and set it aside.
Make the sauce:
Blend the cottage cheese, milk, seasonings, and cornstarch until smooth. You'll add the cheddar later.
Pour the sauce into the pot (without the pasta), add the shredded cheese, and heat it up over medium-low heat, stirring to melt the cheese. When the sauce begins to simmer and the cheese has melted, it's ready. Reduce the heat to the lowest setting.
Add the pasta back into the pot and mix with the cheese sauce. If the sauce is too thick to your liking, add a bit of the reserved pasta water and mix. Serve warm.
Storage:
Once cooled, refrigerate leftovers. To reheat, add a couple of tablespoons of milk or water to reconstitute the sauce and microwave until warm, stopping a few times to stir.