Bring a large pot of water to a boil and salt it. Put ¼ cup olive oil in a large skillet over medium-low heat. When oil is warm, cook garlic just until fragrant, 1 to 2 minutes. Add bread crumbs and red pepper flakes and cook until bread crumbs are golden, 5 minutes or so. Remove and set aside.  Cook broccoli in boiling water until it is soft, about 5 minutes. Remove with a slotted spoon, drain well and chop. Cook pasta in same pot.

Meanwhile, add remaining oil to skillet over medium-low heat. Add broccoli raab and toss well; sprinkle with salt and pepper. When it is warm add garlic and bread crumbs and mix well.
When pasta is done, drain it, reserving a little cooking water. Toss pasta in skillet with broccoli raab mixture, moistening with a little reserved water if necessary. Adjust seasonings and serve with freshly grated Parmesan.