How to Make It
Preheat oven to Bring a large pot of water to a boil with 2 T salt.
Combine the broccoli, 1/4 cup olive oil, 2 t. salt, and 1/2 t. pepper on a sheet pan, spread out, and roast for five minutes. Add the shrimp to the broccoli, toss well, and spread out in one layer. Roast the shrimp and broccoli for 8 to 10 minutes, until the shrimp is cooked.
Meanwhile, cook the pasta in the pot of boiling salted water according to the directions on the package. Set aside 1 1/2 cups of the cooking water before you drain the pasta.
Heat 1/3 cup of olive oil ovr medum heat in a pot large enough to hold the pasta, such as a 12 inch saute pan or a large shallow pot. Add the garlic and cook for one to two minutes, sitrring frequently, until it just begins to turn golden on the edges. Add the red pepper flakes and cok for 30 seconds more. Carefully add the reserved pasta-cooking water to the galic and oil and bring to a boil. Then lower the heat, add 1 t. salt, and simmer for about five mnutes, until the liquid is reduced by about a third.
Add the drained pasta to the garlic oil and toss. Off the heat, add the cooked shrimp and broccoli, plus the parsley and Parmesan, and toss well. Allow the pasta to rest off the heat for five minutes, for the sauce to be absorbed in the pasta, then taste for seasonig and serve warm with extra Parmesan on the side.