Preheat oven to 400°F (200°C) and lightly oil a baking sheet. Wipe mushrooms clean, remove stems, and finely chop the stems.

Heat 2 tbsp olive oil in a skillet over medium heat. Cook the onion and chopped stems for 5 minutes, then add the garlic for 30 seconds. Off heat, stir in the panko, nutritional yeast, thyme, salt, and pepper.

Arrange mushroom caps on the baking sheet. Spoon the filling into each, packing gently and mounding it above the rim. Brush the tops with the 2 tbsp melted vegan butter.

Bake for 18 to 20 minutes until the tops are golden and crisp. Let cool briefly, transfer to a platter, garnish with parsley if using, and serve hot.