Bring a large pot of water to a boil for the pasta.
Heat a few inches of water in a deep skillet and salt it liberally once it boils. Trim the rapini of its tough ends and chop the leaves and florets into bite-size pieces. Cook the rapini about 3 minutes in the skillet then cold shock and pat dry. Dump the water and wipe pan dry.
Peel the casing off the salami and grate it with a box grater. Heat 3 turns of the pan of EVOO to the skillet over medium-high then add salami and stir 1-2 minutes to render and crisp. Add garlic and the rapini, season with salt and chili flakes to taste.
Salt the water for the pasta and cook pasta to 1 minute less than al dente according to package directions. Add 1 cup starchy cooking water to the salami and broccoli rabe, drain spaghetti then toss with rapini and salami. Wilt in lots of torn basil, top with cheese and serve.