Preheat your oven to 350 degrees.
Heat 4 cups of the chicken stock in a Dutch oven until it comes to a boil.
Add the rice and mushrooms to the stock, once it starts boiling again, put the lid on and put in the oven.
Cover and bake for 45 minutes, until most of the liquid is absorbed and the rice is al dente.
Remove from the oven, add the 1 & 1/2 cups of chicken stock, the Parmesan, butter, salt, and pepper, and stir until the rice starts to become creamy. This will take about 2-3 minutes.
Once mixed add the frozen peas at the end. Serve immediately.