Preheat the oven broiler with the rack about 6 inches from the heat. Heat the olive oil in a sauté pan over medium heat. Add the onion and mushrooms and cook for 3-4 minutes or until softened. Dish out the vegetables and set aside. Mix the eggs, milk and parsley together in a bowl. Heat the butter in the sauté pan over medium heat. When the butter has melted and looks foamy, return the cooked vegetables to the pan. Scatter the feta and Parmesan cheeses on top. Pour in the egg mixture and turn the heat to low. Stir once or twice, then cook undisturbed for about 8 minutes or until the bottom has set. Place the pan under the broiler for up to a minute or until the frittata is puffed, golden and crispy on top. Season to taste with freshly ground black pepper.