Add parsley and wine to a food processor and process until finely chopped.Add olive oil to a saucepan and heat over medium-low. Add garlic and shallots and saute until softened, about 3 - 4 minutes.Add wine and cold butter and stir until melted.Add chopped parsley and lemon juice and cook for a minute longer. Remove from heat, season with salt and pepper, then set aside.Preheat oven to 220°C (425°F).Cut mushrooms in half lengthwise. Cut crosshatch marks on inside surface of the mushrooms.Heat olive oil in a grilling pan. When hot, add mushrooms cut side down. Sear then flip over and sear on the other side.Pour in vegetable stock and transfer frying pan to the oven. Roast for 30 minutes.To serve, add parsley sauce to a plate and top with roast king oyster mushroom.