Preheat the oven to 425 degrees F. Bring a pot of salted water to a boil and cook the bucatini according to package directions.
Place the broccoli on the baking sheet and drizzle with 1 tablespoon of olive oil. Sprinkle with salt and pepper. Roast for 15 minutes.
While the broccoli is roasting, heat a large skillet over medium-low heat and add the 5 tablespoons of olive oil. Once hot, add in the sliced garlic and red pepper flakes. Cook, stirring occasionally, until the garlic is just golden. Turn off the heat or keep it very low.
Remove the sheet from the oven and push the broccoli to one side. Place the shrimp in a single layer on the sheet and drizzle with the remaining 1 tablespoon of olive. Sprinkle it with salt and pepper. Roast the shrimp for 6 to 8 minutes, until just opaque and pink.
Toss the bucatini into the garlic oil, coating all the noodles well. Toss the shrimp and broccoli in with the pasta. Toss in the parsley. Spritz on some fresh lemon. Serve with parmesan cheese and extra crushed red pepper flakes!