1. Cook the pasta and broccoli: Bring a large pot of well-salted water to a boil. Add the pasta and cook according to package directions. During the last 2 to 3 minutes of cooking, add the broccoli to the same pot. Before draining, reserve 1½ cups of the pasta water. Drain and set aside.
2. Sauté the garlic: Return the empty pot to medium heat. Add the olive oil, then the minced garlic. Cook for about 30 seconds, just until fragrant but not browned.
3. Blend the sauce: In a blender, combine the sautéed garlic, cottage cheese, Parmesan, 1 cup of the reserved pasta water, salt and pepper. Blend until completely smooth and creamy. The mixture should look glossy and pourable.
4. Combine: Return the pasta and broccoli to the pot. Pour in the blended sauce and toss gently over low heat until evenly coated. Add additional pasta water a splash at a time if needed to loosen the sauce and help it cling.
5. Serve: Taste and adjust seasoning. Finish with extra Parmesan, freshly cracked black pepper and chopped parsley if desired. Serve immediately.
