Slice the onions into thin quarter circles.

Melt the butter in a large frying pan over medium heat.

Add the sliced onions and cook, stirring frequently, for 7–9 minutes, until they begin to brown.

Reduce the heat to medium-low. Add the broth, garlic powder, dried thyme, and black pepper. Stir well, scraping up any browned bits from the bottom of the pan.

Continue cooking for 12–15 minutes, stirring occasionally, until the onions are very soft, deeply browned, and reduced. Taste and add salt as needed, depending on the saltiness of your broth.

While the onions cook, wash and dry the mushrooms. Remove the stems and clean out the centers to create enough room for the filling.

Preheat the oven to 400°F (200°C). Line a baking pan with parchment paper for easier cleanup.

Place the mushrooms hole-side up on the prepared pan.

Spoon a small amount of the onion mixture into each mushroom, filling them tightly.

Sprinkle a small mound of grated cheese over each mushroom.

Bake for 10–15 minutes, until the mushrooms are cooked through and the cheese is melted and browned in spots.

Garnish with fresh parsley or thyme and serve hot.