Put the oil in a deep 10-inch nonstick skillet over medium heat. When it's hot, add the onion and cook, stirring occasionally, until they soften, about 3 minutes.
Add the rice and cook and stir for 2 minutes. Add a little pepper, then the water. Stir and continue cooking until the liquid has almost completely bubbled away.
Use a ladle to begin adding broth, 1/2 cup or so at a time, stirring after each addition. When the broth is just about evaporated, add more. The mixture should be neither soupy nor dry. Keep the heat at medium to medium-high and stir frequently. It should take about 20 minutes to add all of the broth. The rice should be tender but still with a tiny bit of crunch.
Stir in the butter, Parmesan, and peas; continue cooking and stirring until the peas are tender and warmed through. Serve immediately. Makes 4 to 6 servings.