Bring a large pot of salted water to a rolling boil, then add the pasta. Cook until al dente, about 8 minutes, stirring occasionally.
While the pasta cooks, cut the broccoli into bite-sized florets. When the pasta has about 3 minutes left, add the broccoli directly into the boiling water to blanch until vibrant green and slightly tender.
Drain the pasta and broccoli, reserving about half a cup of the starchy cooking water. Set aside.
Heat the olive oil in a large skillet over medium heat until shimmering. Add the minced garlic and cook gently, stirring constantly, until fragrant and golden, about 30 seconds—avoid browning.
Add the drained pasta and broccoli to the skillet, tossing to coat everything evenly in the garlic oil. If the mixture feels dry, splash in a bit of the reserved pasta water to loosen.
Cook together over low heat for another minute, stirring gently, until the flavors meld and the pasta is glossy. Season with salt and red pepper flakes to taste.
If desired, squeeze fresh lemon juice over the pasta just before serving to brighten the flavors.
Serve immediately, garnished with additional red pepper flakes or grated cheese if you like. Enjoy the lively crunch of broccoli paired with fragrant garlic oil coating each strand of pasta.
