Bring a large pot of water to a rolling boil and salt it generously.
Add the broccoli (or cauliflower/broccoli raab) to the boiling water and cook until tender-crisp, about 5-10 minutes depending on the vegetable.
Do not drain the water.
While the vegetable cooks, heat the 1/4 cup (960 ml) of olive oil in a large skillet over medium-low heat.
Add the chopped garlic and cook gently until it sizzles and becomes fragrant, about 1-2 minutes. Be careful not to let it brown.
Keep the skillet on low heat.
Using a slotted spoon, transfer the cooked vegetable directly from the pot into the skillet with the garlic oil.
Turn the skillet heat up to medium-high.
Cook, stirring and gently mashing some of the pieces with your spoon until everything is heated through and well-coated.
Return the water in the pot to a boil and cook the pasta according to package directions until al dente.
Before draining, reserve about 1 cup (240 ml) of the starchy pasta water.
Drain the pasta and add it directly to the skillet with the vegetable mixture.
Add a splash (about 1/4 cup / 960 ml) of the reserved pasta water and toss everything together vigorously. The starchy water will help create a light, creamy sauce that coats the pasta.
Continue to toss, adding more pasta water as needed to keep the dish from being dry.
Season generously with salt and pepper.
Serve immediately, with an extra drizzle of olive oil at the table if you like.
Toss in a large handful of fresh spinach or arugula during the last minute of cooking until it just wilts into the pasta.
Stir in a tablespoon of tomato paste with the garlic to build a deeper, richer flavor foundation for the sauce.
