Bring a large pot of salted water to a boil. When water boils, add pasta and broccoli at the same time and cook according to pasta instructions for al dente. When pasta is almost done cooking, reserve about 1 cup of the pasta water and set aside. Drain pasta and broccoli.
Return the pot to the stove and set heat to high; add 1 tbsp olive oil, when hot, add garlic. Cook until golden, reduce flame to low and add pasta back to the pot.
Mix well, add remaining olive oil, grated cheese, salt and pepper to taste mixing well and smashing any large pieces of broccoli to break up.
Add 1/2 cup of reserved pasta water and mix well adding more if needed.
Serve in pasta bowls with additional grated cheese on the side.
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