Melt the butter in a large skillet over medium-high heat. When the butter is melted and the skillet is hot, throw in the mushroom caps and toss them around for a minute. Remove from the skillet and set aside.
Throw the green onions and garlic in the skillet, saute for a minute and then add the parsley and wine (if you're using it). Stir and cook for 1 to 2 minutes to release all the flavors, then remove from the heat.
Set the mushroom caps on a baking sheet or in a baking dish. Place a chunk of Brie inside of each cap, then pour the parsley mixture all over the tops. Bake until the cheese is melted, about 15 minutes.
Serve the mushrooms straight out of the oven, or at room temperature a little bit later. These are perfect little pop-in-your-mouth delights. You'll love them.