Preheat your oven to 375 degrees. Line a baking sheet with foil and lightly grease.
Snap the stems from the mushroom caps and place the caps onto the baking sheet. Sprinkle the inside of the caps lightly with salt and pepper. Finely chop the mushroom stems.
Heat the olive oil in a pan over medium-high heat. Cook the mushroom stems and chopped onion in the oil for 4 minutes. Add the garlic to the pan and cook for an additional minute.
In a bowl, stir together the softened cream cheese, shredded mozzarella, shredded asiago, parsley, and mushroom mixture until well combined. Fill each mushroom cap with a heaping spoonful of the cream cheese mixture.
In a small bowl, combine the breadcrumbs and parmesan cheese. Dip the cream cheese side of each mushroom into the panko mixture pressing down lightly to cover the tops of the mushrooms with the mixture.
Drizzle the mushrooms with the melted butter and bake for 20-25 minutes or until golden brown.
Don't sweat it if the cheese melts out of the caps a bit. The crispy cheese on the pan makes the mushrooms even better!