In a medium saucepan, melt the butter over medium heat. Add the onion and cook,stirring occasionally, until it begins to soften, about 3 minutes.
Add the broth, increase the heat to medium high, and bring to a boil. Stir in the rice and peas and return to a roiling boil. Cover the pan, reduce the heat to low, and cook 5 minutes. Then stir in the cheese and remove from heat. Cover the pan and let the rice stand until the broth has been absorbed, about 5 minutes.