Preheat the oven to 350 degrees.

Remove the stems from the mushroom caps and set the caps aside. Mince the mushroom stems.

Heat the butter in a small skillet over medium heat. Add the minced mushrooms, onion, and thyme, and cook for 5-7 minutes, or until golden brown and slightly caramelized. Season with freshly cracked black pepper to taste. Set aside to cool.

Combine the panko crumbs, Parmesan cheese, and parsley in a small bowl and mix well.

Mix the Boursin cheese with the cooled onion/mushroom mixture.

Add half of the panko mixture to the Boursin cheese mixture and mix until evenly combined.

Drizzle the mushroom caps with olive oil until evenly coated. Stuff the mushroom caps with the Boursin mixture.

Dip the cheesy tip of the mushrooms in the remaining panko mixture, then place them on a small baking sheet.

Bake the mushrooms for 20 minutes, or until they are tender and the cheese is gooey. Optionally, place them under the broiler for a minute or two for a more golden topping, watching carefully to prevent burning.