Bring a large pot of water to a boil. Cook the broccoli about 2–3 minutes until it just starts to soften. Remove the broccoli with a slotted spoon and set aside, so you can then use the water for boiling the spaghetti.
Add the pasta to the boiling water and cook according to package directions. Just before straining the pasta, reserve 1/2 cup of the cooking water. Set the pasta aside in a strainer for a couple minutes and return the pot to the stove.
Set the pot over low heat and drizzle in a little bit of olive oil. Add the garlic and sauté lightly, about 1–2 minutes, mixing frequently so it doesn’t burn. Add the cooked broccoli to the pot and sauté another 2 minutes.
Pour the pasta water, Broccomole, and cooked pasta into the pot. Mix well until the pasta is evenly coated.
Season the broccoli pasta with salt and pepper to taste. Optionally, sprinkle with Parmesan just before serving.