Cut the florets off the broccoli, and cut the stalk and stems into ½-inch pieces. Steam the broccoli for 5 minutes, adding first the stalk and stems, then the florets for only 2 minutes.
Thinly slice the garlic. Warm a large skillet with high sides over medium heat, add the olive oil and garlic slices or paste and stir for a minute. Add the steamed broccoli and cook all together for 3 - 4 minutes, until the broccoli is tender but still al dente. Stir in the lemon zest. Remove and set aside.
Boil the pasta in well-salted water according to package directions, drain and reserve a cup of the pasta cooking liquid. Transfer the drained pasta to the broccoli skillet and toss all together, adding about half a cup of the pasta water to make the mixture juicy and succulent.
Season with sea salt, black pepper, and red pepper flakes. Heat for a minute or two and serve immediately, tossed or topped with the grated cheese.