Melt the butter in a large skillet over medium heat. Add the onion and mushrooms and cook until the mushrooms release their liquid and start to brown.
Stir in the garlic and cook for one minute until fragrant.
Add the wild rice and broth to the skillet. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 45 minutes until the rice is tender and most of the liquid is absorbed.
Stir in the frozen peas and cook for 3 minutes until heated through.
Pour in the heavy cream and Parmesan cheese. Stir until the sauce thickens slightly and coats the rice evenly.
Season with salt and black pepper to taste, then remove from heat and sprinkle with fresh parsley before serving.