Pop the stems from the mushrooms and reserve for another use. Using a melon baller or spoon, gently scoop out any remaining stem from inside the mushroom caps. Brush the outside of the caps with 1 tablespoon of the oil. Set the caps aside.
Put the leftover stuffing, parsley, butter, egg, a large pinch of salt and a few grinds of pepper in a large bowl. Use your hands to combine the mixture and squeeze it together.
Pack each mushroom with an equal amount of filling and transfer the filled mushrooms to a rimmed baking sheet. Drizzle the tops with the remaining 1 tablespoon oil. Bake until the mushrooms are tender and the filling is brown and crispy on top, about 15 minutes. Let cool 5 minutes before removing from the baking sheet.
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