4 tablespoons unsalted butter
24 large white button mushrooms (about 2-1/2 inches wide; 2-1/2 lb. total), stemmed; stems finely chopped and caps wiped clean
¾ cup shredded or grated Parmesan (3 ounces)
3/4 cup panko
1/3 cup mayonnaise
1/4 cup finely chopped fresh flat-leaf parsley
Freshly ground black pepper
1-1/2 tablespoons extra-virgin olive oil
Position a rack in the center of the oven and heat the oven to 400°F.
Melt the butter in a 10-inch nonstick skillet over medium heat. Set aside 2 Tbs. of the melted butter in a small bowl. Add the mushroom stems and 1/4 tsp. salt to the skillet and cook, stirring often with a wooden spatula, until tender, about 5 minutes. Let cool to room temperature.
Meanwhile, add 2 Tbs. of the Parmesan and the panko to the reserved melted butter and mix thoroughly; set aside.
In a medium bowl, stir together the remaining Parmesan, the mayonnaise, parsley, and 1/4 tsp. black pepper. Add the mushroom stems and mix until well combined.
In a large bowl, toss the mushroom caps with the oil. Fill each mushroom cap with a rounded teaspoon of the filling and top each with about 1 tsp. of the panko mixture. Place on a large rimmed baking sheet with space in between. Bake until tender and the topping is golden-brown, about 25 minutes. Cool briefly before serving.