01 - Bring a large pot of generously salted water to a rolling boil. Add the mafaldine and cook according to package directions until al dente. Reserve 1/2 cup of starchy pasta water before draining.
02 - During the last 3–4 minutes of the pasta cooking time, add the broccoli florets directly to the boiling pasta water. Drain the pasta and broccoli together.
03 - In a large skillet over medium heat, warm the olive oil and butter together. Add the minced garlic and chili flakes if using, and sauté for about 1 minute until fragrant but not browned.
04 - Add the lemon zest, lemon juice, blanched broccoli, and drained mafaldine to the skillet. Toss thoroughly to coat, then sprinkle in the grated Parmesan, stirring until a silky sauce forms. If the pasta appears dry, incorporate the reserved cooking water a splash at a time.
05 - Season with salt and freshly ground black pepper to taste. Remove from heat and fold in the chopped parsley.
06 - Divide among warm plates immediately. Garnish with additional shaved Parmesan and a sprinkle of lemon zest if desired. Serve at once.