Preheat the oven to 425°F (220°C). Bring a large pot of salted water to a boil.
Cook the bucatini according to package directions until al dente, then reserve about 1/2 cup pasta water and drain.
Toss the broccoli florets with 1 tablespoon olive oil, 1/2 teaspoon salt, and 1/2 teaspoon freshly cracked black pepper on a baking sheet and roast for 15 minutes.
While broccoli roasts, heat a large skillet over medium-low and add the 5 tablespoons olive oil. Add the sliced garlic and crushed red pepper flakes and cook, stirring occasionally, until the garlic is just golden—do not burn it. Keep the heat very low or turn it off to prevent further browning.
Remove the baking sheet from the oven, push the broccoli to one side, place the shrimp in a single layer on the sheet, drizzle with the remaining 1 tablespoon olive oil, and season with salt and pepper. Roast the shrimp 6 to 8 minutes, until opaque and pink.
Add the cooked bucatini to the skillet with the garlic oil and toss to coat, adding a splash of reserved pasta water if needed to loosen the sauce.
Toss the roasted shrimp and broccoli with the bucatini, stir in the chopped parsley, and adjust seasoning to taste.
Squeeze lemon over the pasta and serve with grated Parmesan and extra crushed red pepper flakes if desired.
