Heat the olive oil in a large nonstick frying pan and add the gnocchi. Pan-fry for about 8 minutes, moving frequently, until crisp and golden.
Meanwhile, toss the tomatoes with the basil leaves and torn mozzarella, season to taste and arrange on 4 serving plates.
Add the chorizo to the pan of gnocchi for the final 1–2 minutes of cooking, until slightly crisp and golden. Scatter the gnocchi and chorizo over the salads and drizzle with a little balsamic vinegar to serve.