Cook the pasta. Bring a large pot of salted water to a boil. Cook shells to al dente per package directions. Reserve 1 cup of pasta water, then drain.
Prep the sweet potato (zero-prep method). Pierce a sweet potato with a fork, microwave 5–7 minutes until tender, then scoop out the flesh. Alternatively, use 1 cup canned sweet potato purée.
Blend the sauce. In a blender, add sweet potato, milk, cheddar, mozzarella/Jack, butter, Dijon or miso, garlic powder, onion powder, paprika, 1/2 teaspoon salt, and a few grinds of pepper. Blend until completely smooth and glossy, 30–60 seconds. If too thick, thin with a splash of reserved pasta water or milk.
Warm it up. Return the drained pasta to the pot over low heat. Pour in the sauce and toss. Add a splash of pasta water to loosen if needed. Heat gently for 1–2 minutes until the cheese is fully melted and the sauce is silky. Don't boil—cheese gets cranky.
Taste and finish. Adjust seasoning with salt, pepper, paprika, or a dash of hot sauce. If you want luxurious gloss, stir in 1–2 tablespoons cream cheese. Serve hot, with extra black pepper on top.