Preheat your oven to 375°F.
In a large skillet, heat the olive oil over medium heat. Add the sliced onions and salt, cooking until they are soft and caramelized, about 15-20 minutes. Stir occasionally to prevent burning.
Once the onions are caramelized, add black pepper, thyme, balsamic vinegar, and garlic powder. Mix well and cook for an additional 2 minutes. Remove from heat and let cool slightly.
In a mixing bowl, combine the caramelized onion mixture, grated Gruyère cheese, breadcrumbs, and chopped parsley. Mix until well combined.
Stuff each mushroom cap with the onion and cheese mixture, pressing down gently to pack it in. Place the stuffed mushrooms on a baking sheet lined with parchment paper.
Bake in the preheated oven for 20-25 minutes, or until the mushrooms are tender and the tops are golden brown.
Remove from the oven and let cool for a few minutes before serving.