Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions. About 3 minutes before the pasta is done, add the broccoli florets to the boiling water. Drain the pasta and broccoli together and set aside.
In a large skillet, heat the oil over medium heat. Add the minced garlic and sauté for 1-2 minutes until fragrant, being careful not to burn it.
Add the drained pasta and broccoli to the skillet. Toss well to coat with the garlic-infused oil. Season with salt and pepper to taste.
Sprinkle the grated cheese over the pasta and broccoli. Stir to combine until the cheese is melted and everything is evenly distributed.
Serve warm and enjoy!