01 - Bring a large pot of generously salted water to a rolling boil. Add the mafaldine and cook according to package directions, but subtract 2 minutes from the recommended time so the pasta finishes al dente.
02 - Three minutes before the pasta is done, add the broccoli florets directly into the pasta water. Reserve ½ cup of the starchy cooking water, then drain the pasta and broccoli together in a colander.
03 - While the pasta cooks, warm the olive oil in a large skillet over medium heat. Add the sliced garlic and chili flakes if using, and sauté for 1 to 2 minutes until fragrant and just golden, taking care not to let the garlic brown.
04 - Transfer the drained mafaldine and broccoli to the skillet. Pour in the lemon juice and scatter the zest over the top. Add a splash of the reserved pasta water and toss vigorously to coat, adding more water as needed to build a silky, clinging sauce.
05 - Sprinkle the grated Parmesan over the pasta and toss until the cheese melts into the sauce and evenly coats every ribbon. Season with salt and freshly ground black pepper to taste.
06 - Divide among warmed plates immediately. Finish with an extra shower of Parmesan and a scattering of fresh basil or parsley if desired. Serve at once while the sauce is still glossy.