Heat 1 Tbs. olive oil in a large pot over medium-high heat. Add half the pasta and cook, stirring often, until it is a deep golden brown, 2 to 4 minutes. Remove noodles to a large plate and repeat with another 1 Tbs. oil and the remaining pasta; set aside.
Heat the remaining 1 Tbs. oil the same large pot over medium-high. Add the onion and cook, stirring often, until starting to soften, about 5 minutes. Add the chickpeas and cook, stirring occasionally, until starting to brown in spots, about 3 minutes. Add the chorizo and garlic; cook, stirring, 1 minute. Stir in the spinach and tomatoes; cook, tossing, until the spinach is wilted, about 2 minutes.
Add the pasta and water, cover the pot and cook 3 minutes. Remove cover, stir and cook until the pasta is tender and most of the liquid has been absorbed or cooked off, about 5 more minutes. Stir in salt and pepper. Serve topped with a sprinkling of oregano.