In a saute pan, heat the oil. Add the onions. Season with salt and pepper. Saute for 1 minute. Add the mushrooms and continue to saute for 2 minutes. Season with salt and pepper. Stir in the garlic and peas. Saute for 1 minute and remove from the heat. Turn the mushroom mixture into the Bolognese and mix well. Toss the pasta with the sauce. Mound the pasta into shallow bowls and garnish with cheese and parsley.