Heat 1 tablespoon of olive oil in a skillet over medium-high heat. Cook and stir the chorizo, garlic, and onion in the hot oil until the chorizo has browned and no longer pink, and the onion has softened, about 10 minutes. Pour off any excess grease, then
transfer to a bowl.
Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the rotini, and return to a boil. Cook uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the
bite, about 8 minutes. Drain well in a colander set in the sink.
Pour the water and 2 tablespoons olive oil into the skillet that the chorizo was cooked in. Bring to a boil over high heat, then add the broccoli rabe, cover, and cook until tender, about 4 minutes. Uncover, and stir in the chorizo mixture; bring to a simmer.
Toss the pasta with the chorizo mixture in a large bowl. Season to taste with salt and black pepper, and sprinkle in the Parmesan cheese. Stir gently before serving.