Bring a large pot of salted water to a rolling boil. Once bubbling vigorously, add the pasta and cook for about 8 minutes, stirring occasionally. Test a strand—it's ready when it’s just al dente, with a slight bite.
While the pasta cooks, prepare the broccoli by chopping it into small, uniform florets. Mince the garlic cloves finely, ensuring they’re ready to sauté.
Drain the pasta, reserving about 1/4 cup of the starchy cooking water. Set aside. In a large skillet, heat the olive oil over medium heat until it shimmers and begins to gently bubble.
Add the minced garlic to the skillet. Sizzle for about 30 seconds until fragrant and just starting to turn golden—be careful not to burn it, as burnt garlic turns bitter.
Add the broccoli florets to the skillet. Toss to coat them evenly with the garlic oil and cook for 3-4 minutes, stirring occasionally, until the broccoli turns bright green and is just tender with a slight crunch.
Transfer the drained pasta into the skillet with broccoli. Pour in a splash of the reserved pasta water and toss everything together over low heat for about 1 minute. This helps the flavors meld and creates a silky sauce.
Season with salt, freshly cracked black pepper, and red pepper flakes if using. Squeeze some lemon juice and zest the lemon over the pasta for brightness. Toss again to distribute evenly.
Finish with a little extra olive oil drizzled over the top for shine and richness. Give everything a final toss to coat thoroughly.
Serve the pasta immediately while hot, garnished with additional lemon zest or cheese if desired. Enjoy the simple harmony of garlic, broccoli, and olive oil in every bite.
