Bring a large pot of water to a rolling boil and generously salt it. Add the pasta and cook until just al dente, about 8 minutes. Reserve a cup of pasta water, then drain and set aside.
While the pasta cooks, trim the broccoli into bite-sized pieces. Heat the olive oil in a skillet over medium heat until it shimmers and begins to gently bubble.
Add the broccoli to the skillet and sauté for 3-4 minutes, stirring often, until it turns bright green with a slight char on the edges.
Add the sliced or crushed garlic to the skillet with the broccoli. Cook for 1-2 minutes until fragrant, the garlic just begins to turn golden, filling your kitchen with a sweet, toasty aroma.
Drain the pasta, then add it directly to the skillet with the broccoli and garlic. Toss everything together, adding a splash of reserved pasta water as needed to create a silky, glossy sauce that coats the noodles and vegetables evenly.
Finish by zesting and squeezing the lemon over the pasta, then sprinkle with red pepper flakes, salt, and pepper to taste. Toss again to combine all the flavors beautifully.
Remove from heat and serve immediately, the pasta should be glossy with vibrant broccoli and fragrant garlic, ready to enjoy with a drizzle of olive oil or extra lemon if desired.
