Preheat the oven to 450°F.
In a baking dish, combine 1 1/2 lbs broccoli florets, 6–8 smashed garlic cloves and 2 tablespoons extra virgin olive oil; season with kosher salt and fresh pepper and toss to coat. Spread the broccoli in a single layer.
Roast for about 20 minutes, tossing once halfway through, until the broccoli is browned and tender.
Meanwhile, bring a large pot of salted water to a boil.
Add 8 oz pasta and cook according to package directions until al dente.
Before draining, reserve 1 cup of the pasta cooking water. Drain the pasta.
Add the drained pasta to the baking dish with the roasted broccoli and garlic and toss to combine.
Add 1/2 cup of the reserved pasta water and 1/4 cup fresh grated Pecorino Romano; toss until the pasta is coated, adding more reserved pasta water if needed to reach the desired consistency.
Taste and adjust with kosher salt and fresh pepper as needed, then serve immediately.