How to Make It
In a medium saucepan, cook the olive oil and chorizo over moderate heat, stirring occasionally, until the chorizo is tender, about 10 minutes. Using a slotted spoon, transfer to a small bowl. Add the shrimp, garlic and a generous pinch of salt to the saucepan and cook over low heat, stirring occasionally, until the shrimp are cooked through, 8 to 10 minutes. Using a slotted spoon, transfer the shrimp and garlic to the bowl with the chorizo. Reserve the oil.
Meanwhile, in a large pot of salted boiling water, cook the pasta until al dente. Drain well.
In the pot, combine the tomatoes and 1/2 cup of the reserved chorizo oil; discard the remaining oil. Cook over moderately high heat, stirring occasionally, until the tomatoes just start to soften, about 3 minutes. Add the shrimp mixture and the pasta and cook, tossing, until hot and the pasta is coated in a light sauce, about 2 minutes. Season generously with salt and pepper, then stir in the torn basil. Transfer to bowls, garnish with more basil and serve right away.