Clean the mushrooms with a damp cloth and gently remove the stems. Set aside the caps and finely chop the stems.
In a large skillet over medium heat, add the olive oil and butter. Once melted, stir in the chopped onions and cook for about 5 minutes until translucent. Add the minced garlic and chopped mushroom stems, cooking for an additional 3-4 minutes until softened.
Sprinkle the flour over the mixture and stir well to combine. Cook for about 1 minute. Gradually pour in the broth while continuously stirring to prevent lumps. Add the dried thyme, rosemary, salt, pepper, and soy sauce if using. Bring the mixture to a simmer and cook for about 5-7 minutes until thickened.
Preheat your oven to 375. Using a spoon, generously fill each mushroom cap with the savory gravy mixture. Arrange the stuffed caps on a baking sheet lined with parchment paper.
Bake in the preheated oven for 15-20 minutes, or until the mushrooms are tender and the tops are golden brown.
Once out of the oven, let them cool for a couple of minutes. Garnish with fresh chopped parsley before serving.