Boil the water: Bring a large pot of salted water to a rolling boil. Use about 1 tablespoon of salt for every 4 quarts of water.
Cook the pasta: Add your pasta to the boiling water and cook according to package directions, minus 2 minutes. You want it slightly underdone since it'll finish cooking later.
Add the broccoli: During the last 3-4 minutes of pasta cooking time, toss in the broccoli florets. They should be bright green and tender-crisp.
Reserve pasta water: Before draining, scoop out about 1 cup of the starchy pasta water. This is liquid gold for creating a silky sauce!
Drain everything: Drain the pasta and broccoli together in a colander.
Sauté the garlic: While the pasta cooks, heat olive oil in a large skillet over medium heat. Add minced garlic and red pepper flakes, cooking for about 1 minute until fragrant but not browned.
Combine it all: Add the drained pasta and broccoli to the skillet with the garlic oil. Toss everything together over low heat.
Add lemon and cheese: Remove from heat and add lemon zest, lemon juice, and Parmesan cheese. Toss well to combine.
Adjust consistency: Add reserved pasta water, a little at a time, until you reach your desired sauce consistency. The starch helps everything cling together beautifully.
Season and serve: Taste and adjust seasoning with salt and pepper. Garnish with fresh herbs and extra Parmesan if desired.