Fill a large pot with 4 quarts of water and about 2 tablespoons salt. Bring to a boil over high heat.
Add broccoli to the boiled water, bring it back up to a boil, then cook for 4 minutes. Add in your pasta and cook according to the package instructions, stirring occasionally to make sure it’s not sticking to the pot. Reserve at least 1 cup of pasta water, then drain your pasta/broccoli.
Wipe out the skillet until dry. Return the pot over medium heat, add the oil, garlic, and pepper and cook for 1 minute, stirring often, until fragrant.
Add the drained pasta/broccoli into the pan along with 1 cup pasta water and cheese (if using). If not using cheese, add an additional ½ teaspoon salt. Cook for about 1-2 more minutes, stirring constantly, or until the liquid reduces and forms more of a glossy sauce. Taste and add more salt, if needed. This depends a lot on how salty your pasta water was and whether or not you added cheese!
Serve topped with black pepper and a drizzle of your best olive oil. If using cheese, sprinkle some more on top if you have it.