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