1. Preheat the oven to 400°F (200°C) and prepare two large baking sheets. Arrange the puff pastry squares spaced 1-2 inches apart, no more than six per pan.
2. Use a fork to poke small holes on the surface of each puff pastry square, taking care not to pierce all the way through.
3. Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Sauté the shallot and garlic for 1-2 minutes until fragrant.
4. Add the sliced mushrooms, remaining olive oil, and the dried herbs and season with salt and pepper. Cook for 2 minutes until mushrooms begin to soften.
5. Pour in the white wine (or brandy/chicken broth) and cook for another 4-5 minutes until most liquid evaporates and mushrooms are tender.
6. Turn off the heat and stir in the goat cheese, Parmesan, and parsley. Mix until the goat cheese melts, thickening the filling.
7. Spoon the filling generously onto each puff pastry square. Optionally, pinch the corners or edges slightly to shape the squares and reduce excessive puffing, or leave them flat to puff naturally.
8. Brush the exposed pastry edges with the egg wash, avoiding the filling, to achieve a golden finish.
9. Bake for 25-30 minutes or until the pastries are golden brown and puffed. Serve warm.