Remove and discard spinach stems; chop coarsely and set aside. Cook pasta. Just before pasta is done, stir in spinach. Cook uncovered, stirring to distribute spinach; just until water returns to a full boil. Drain pasta and spinach.
While pasta is cooking, heat oil in a wide frying pan over medium heat. Stir in garlic and chilies. Cook, uncovered, until garlic turns opaque (about 2 minutes).
Add pasta and spinach to pan; mix. Mix in Parmesan cheese. Serve.