In a soup pot or dutch oven, melt the butter over medium heat. Add the onion and sauté until it becomes lightly golden. In a separate pot, heat the stock until it reaches a simmer.
Once the onion is ready, add 3 cups of the simmering stock, the rice, the bag of frozen peas, and a good pinch of salt. Cover the pot and and cook at a low boil for about 20 minutes, stirring occasionally, until the rice is just tender. If the soup is too thick, thin it slightly with the remaining stock; it should be thick but not porridge. When the rice is ready, add the grated Parmesan and taste for salt. Serve.