Heat the chicken broth in a medium saucepan, then cover and keep warm on low heat.
Melt the butter in a large saucepan over medium heat and add the olive oil. Add the onions and saute, stirring occasionally, under tender and translucent, 8 to 10 minutes. Add the mushrooms and garlic and saute, stirring occasionally, until the mushrooms are tender and the juices have evaporated, 10 to 12 minutes.
Next, add the rice and stir to incorporate with the vegetables, then immediately add the white wine. Cook, stirring often, until the liquid is absorbed, about 2 minutes. Add 1 cup of the broth to the pan and simmer over medium-low heat, stirring often, until the liquid is absorbed, 3 to 4 minutes. Continue to cook, adding broth by the cupful and stirring often, until the rice is tender and creamy, 28 to 32 minutes. Stir in the Parmesan and peas. Add salt and pepper to taste.