Bring a large pot of water to a boil; add the salt, then the rabe. Cook for 3 minutes. Remove to an ice water bath with slotted spoon or spider and reserve. Bring the water back to a boil. Cook the pasta to al dente, reserving 1 cup of starchy cooking liquid just before draining.
Meanwhile, heat the EVOO in large skillet over medium-high heat. Add the sausage and brown, about 5-6 minutes.
Place half of the chickpeas in a food processor with a splash of water and puree. Add the garlic to the sausage and cook 1 minute. Add the puree and the remaining whole chickpeas and reserved broccoli rabe. Season with salt, pepper and thyme and heat thorough. Add the tomatoes and stir, then reduce the heat to simmer. When the pasta is done, add the reserved cooking liquid to the sauce before draining.
Add the drained pasta back to the pot along with the butter and cheese. Toss to coat, then add the sauce and stir to combine. Serve immediately.
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