While your water comes to a boil, blend the cottage cheese, steamed cauliflower, and 1 cup of parmesan in a food processor or blender until completely smooth and creamy. This sauce base is the foundation of the dish, so blend it thoroughly to ensure a silky texture without any lumps. Set the blended sauce aside in a bowl.
Bring a large pot of salted water to a rolling boil. Add the cavatelli pasta and cook according to package directions until al dente, usually 8-10 minutes. Reserve 1 cup of pasta water before draining—this starchy liquid will help create a silky sauce consistency when combined with your other ingredients. Drain and set aside.
While the pasta cooks, heat the olive oil in a large skillet over medium heat. Add the minced garlic and cook for about 1 minute until fragrant, stirring constantly to prevent browning. Add the broccoli florets and spinach to the pan, stirring frequently. Cook for 4-5 minutes until the broccoli is tender-crisp and the spinach is wilted. I like to keep the broccoli slightly firm rather than fully soft so it maintains some texture in the final dish.
Add the cooked pasta from Step 2 and shredded chicken to the vegetable mixture in the skillet. Pour in the blended sauce from Step 1 along with 1/2 cup of the reserved pasta water, stirring gently to combine everything evenly. Cook over medium heat for 3-4 minutes, stirring occasionally, until the sauce coats all the pasta and the mixture is heated through. If the sauce seems too thick, add more pasta water a tablespoon at a time to reach your desired consistency.
Remove the skillet from heat and stir in the remaining 1/2 cup parmesan cheese. Season generously with freshly ground black pepper, red pepper flakes, and a sprinkle of lemon zest for brightness. Taste and adjust seasonings as needed—I find the lemon zest really lifts the flavors and prevents the dish from feeling heavy despite all the protein and creaminess.
Divide the pasta into bowls or plates and top with additional parmesan cheese and a crack of fresh black pepper. Garnish with fresh parsley for color and a hint of herbaceous flavor. Serve immediately while warm.