Fill the large pot with water, add a generous pinch of salt, and bring to a rolling boil.
Add the pasta to the boiling water and cook until just al dente, about 8-10 minutes, stirring occasionally to prevent sticking.
While the pasta cooks, cut the broccoli into small florets and mince the garlic cloves finely.
Once the pasta is nearly done, heat the olive oil in a frying pan over medium heat until shimmering, and add the minced garlic.
Sauté the garlic until golden and fragrant, about 30-40 seconds, stirring constantly to prevent burning.
Add the broccoli florets to the pan with garlic and toss to coat in the oil. Cook for 3-4 minutes until bright green and slightly tender but still crisp.
Drain the pasta, reserving about half a cup of starchy pasta water, then add the pasta directly to the pan with broccoli and garlic.
Toss everything together over medium heat, pouring in a splash of the reserved pasta water to loosen the mixture into a glossy sauce.
Season with salt and freshly cracked pepper, tasting and adjusting as needed. If using lemon, add a squeeze of lemon juice or zest now for brightness.
Give everything a final toss, allowing the flavors to meld for a minute or two, then remove from heat.
Serve immediately, garnished with a drizzle of olive oil or extra lemon if desired, and enjoy the vibrant, comforting flavors.
