Heat the olive oil in a large skillet over medium-high heat. Add the mushrooms, 1/2 teaspoon salt and a few grinds of pepper and cook, stirring occasionally, until the mushrooms are softened and have released most of their liquid, 7 to 8 minutes. Add the garlic and cook, stirring occasionally, until soft and fragrant, about 1 minute. Stir in the cream cheese and cook until melted and evenly coating the mushrooms. Stir in the mozzarella, 1/2 cup of the panko and 1/4 cup of the Parmesan until combined. Transfer to an 8-inch square baking dish.
Combine the parsley, butter and remaining 1/2 cup panko and 1/4 cup Parmesan in a medium bowl. Sprinkle over top of the mushrooms and bake until the breadcrumbs are light golden brown, 25 to 30 minutes.
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