In a large pot of boiling salted water, cook the pasta al dente according to package instructions. Reserve ½ cup of the cooking water, drain and set aside.

To the bowl of a food processor or blender, add the cottage cheese, cornstarch, salt, pepper, mustard powder, and paprika. Blend until smooth. Add the milk and pulse a few times to combine.

Transfer the cottage cheese mixture to the same pot used to cook the pasta and heat over medium-high heat and bring to a low boil. Continue whisking until thickened, about 1 minute.

Stir in the cheese and ¼ cup of the reserve pasta water until the cheese is melted. Add the cooked pasta and toss to fully coat. Add more pasta water to adjust if needed, and serve immediately.