Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve ½ cup of pasta water, then drain.
Add the cottage cheese, milk, garlic powder, paprika, salt, and pepper to a blender. Blend until completely smooth and creamy.
Pour the blended mixture into a saucepan over low heat. Stir in the shredded cheddar cheese and cook until melted and smooth.
If the sauce is too thick, add a splash of the reserved pasta water until you reach your desired consistency.
Add the cooked pasta to the sauce and stir until evenly coated. Mix in any optional vegetables if using.
Serve immediately with extra cheddar cheese, black pepper, and fresh parsley if desired.