Separate the mushroom stems from the caps. Finely chop the stems (cutting and discarding the rough ends) and set aside the caps.
In a small skillet, melt the butter over low heat and sauté the onion in the butter until soft. Add the mushroom stems and cook until the liquid evaporates (about 5 min). Remove from heat and add the cheese, mixing well. Stir in the seasonings.
Brush the mushroom caps lightly with olive oil. Fill each with the cheese mixture. Place on a baking sheet and brush with the remaining olive oil.
Bake for 10 minutes, or until lightly browned. Serve hot.
Notes
Substitute feta cheese for the goat cheese if you wish.