Preheat your oven to 350°F.
Cook the chickpea pasta according to package directions, aiming for al dente. It will continue cooking in the oven so pulling it a minute early is even better. Drain well and pour into the prepared baking dish.
While the pasta cooks, add the milk, cottage cheese, Greek yogurt, cheddar cheese, parmesan, nutritional yeast, paprika, garlic powder, salt, and pepper to a blender. Blend on high for about 60 seconds until completely smooth and creamy with no lumps. Taste the sauce and adjust seasoning before it goes on the pasta.
Pour the blended sauce over the cooked pasta in the baking dish. Add the broccoli florets. Stir everything together until the pasta and broccoli are fully coated in the sauce.
Bake uncovered for 25 minutes until the top is lightly golden and the sauce is bubbling around the edges.
Let it rest for 5 minutes before serving. The sauce will thicken slightly as it cools and that is exactly what you want.