Adjust the oven rack to about 6 inches from the broiler and preheat the broiler. Set a 2-quart broiler-safe baking dish or oven-safe skillet nearby.
In a blender, combine cottage cheese, milk, Dijon, cornstarch, garlic powder, salt, and pepper. Blend until completely smooth and silky, about 30 seconds. Transfer the mixture to a bowl and refrigerate for 10 minutes to lightly thicken while you start the pasta.
Bring a large pot of well-salted water to a boil. Add the pasta and cook until just shy of al dente (about 1 minute less than package directions). Reserve 1/2 cup of the starchy cooking water, then drain.
Return the empty pot to the stove over medium heat. Pour in the chilled cottage cheese mixture and add 3/4 cup shredded cheddar. Whisk and cook until the cheese melts and the sauce gently steams and begins to thicken at the edges, 3 to 4 minutes. If it tightens too quickly, loosen with a splash of reserved pasta water.
Fold the drained pasta into the sauce and simmer together for 1 minute so it absorbs some of the cheesy goodness. Turn off the heat and let the pot stand for 2 minutes to allow the sauce to settle and cling.
Scrape the mac and cheese into the broiler-safe dish (or keep it in the oven-safe skillet). Scatter the remaining 1/4 cup cheddar over the top and broil just until the surface is spotty-brown and bubbling, 1 to 2 minutes. Watch closely to prevent over-browning.
Serve hot. If the sauce thickens as it sits, stir in a tablespoon or two of the reserved pasta water or milk to bring it back to creamy.