Heat the olive oil in a large skillet over medium-high heat. Add the chorizo and cook, stirring occasionally, until golden and crisp, about 3 minutes. Remove to a plate using a slotted spoon. Add the pasta to the skillet and season with 1/4 teaspoon salt and a few grinds of pepper. Cook, stirring constantly, until toasted, about 3 minutes.
Add the paprika and garlic to the skillet. Cook, stirring, 1 minute. Add 2 cups water, the green beans, olives and chorizo; nestle the clams in the skillet. Cover and cook until the pasta is tender and the clams open, 8 to 10 minutes. (Discard any unopened clams.) Stir in the piquillo pepper and parsley. Serve with lemon wedges.