Pulse the spinach in a food processor until very finely chopped; set aside. In a medium saucepan, heat broth and ½ cup water and leave over low heat.
Heat oil in a large saucepan over medium heat. Add onion and sauté until soft, about 5 min. Add rice and salt; stir to coat rice with oil. Stir in wine and cook until absorbed, 1 min.
Add about ¾ cup broth and stir constantly, until broth is absorbed. Continue adding broth, about ¾ cup at a time, stirring occasionally; let rice absorb broth before adding it again (risotto should be gently simmering as you stir), 18 to 22 min.
With the last addition of broth, stir in the spinach, peas and cheese until cheese is just melted, about 1 min.Serve immediately with extra cheese.
Make sure to use low-sodium chicken broth when making risotto.