Preheat and prep. Heat the oven to 375°F (190°C).
Lightly grease a 9x13-inch baking dish or similar casserole.
Cook the pasta. Boil pasta in well-salted water until just shy of al dente. Drain and set aside. It will finish cooking in the sauce.
Blend the base. In a blender, combine cottage cheese, milk, mustard, garlic powder, paprika, 1 cup shredded cheddar, Parmesan, 1/2 teaspoon salt, and a few grinds of pepper.
Blend until completely smooth and creamy.
Optional roux for extra thickness. In a saucepan, melt butter over medium heat. Whisk in flour and cook 1 minute. Slowly whisk in the blended mixture and simmer 2–3 minutes until slightly thickened.
If skipping the roux, warm the blended sauce gently in a pot until steamy.
Add a touch of tang. Off the heat, stir in Greek yogurt or sour cream if using. Taste and adjust seasoning. You want it a bit salty so it seasons the pasta.
Combine with pasta. Toss the drained pasta with the sauce and another 1/2 cup cheddar.
Transfer to the prepared baking dish.
Add topping. Mix breadcrumbs with olive oil or melted butter and a pinch of salt. Sprinkle over the pasta along with the remaining 1/2 cup cheddar.
Bake. Bake 15–20 minutes, until the top is golden and the edges are bubbling. Let it rest 5 minutes so the sauce sets slightly.
Serve. Spoon into bowls and add a crack of black pepper or a sprinkle of chives if you like.