Bring broth to a boil in a medium saucepan, add the shrimp. Turn off heat, cover and let stand until opaque, about 3 minutes.
Using a slotted spoon transfer the shrimp to a bowl, cover and set aside. Cover broth to keep warm.
Heat oil in a heavy skillet over a medium heat, add the onions and garlic. Sauté for about 3 minutes. Add the rice and cook, stirring for about 2 minutes. Add about ¾ cup of the warm broth, wait until absorbed. Keep adding the broth, ¾ cups at a time until all the broth is absorbed and the rice is just tender, about 25 minutes.
During the last 5 minutes add the spinach, adding in batches so that each batch wilts before you add the next, stir in the shrimp and basil, and ½ cup of cheese. Season with salt and pepper.
Spoon the risotto into shallow bowls and top with additional cheese. Serve.