Warm the vegetable broth in a saucepan over low heat and keep it gently simmering while you cook.
Heat the olive oil and 1 tablespoon of butter in a large skillet over medium heat. Add the diced onion and cook for 3 minutes until it softens.
Stir in the minced garlic and sliced mushrooms. Cook for 5 minutes until the mushrooms release their liquid and start to brown.
Add the Arborio rice and stir for 2 minutes so the grains are coated and lightly toasted.
Ladle in about 1 cup of warm broth. Stir often until the liquid is mostly absorbed. Repeat with the remaining broth, one cup at a time, waiting until each addition is absorbed before adding more.
When the rice is tender and creamy, stir in the frozen peas, salt, and black pepper. Cook for 2 minutes until the peas are heated through.
Remove the skillet from the heat. Stir in the remaining tablespoon of butter and the grated Parmesan until everything is melted and combined.
Sprinkle with chopped parsley before serving.