Wild Mushroom Onion Galette with Brie

Name: Wild Mushroom Onion Galette with Brie
Ingredients: 1 large onion - peeled and sliced; 1 large shallot - peeled and sliced; 2 tablespoons unsalted butter; 2 tablespoons olive oil; 1 1/2 cups mixed wild mushrooms (we used beech, crimini, and oyster) - cleaned and chopped; 1/2 cup dried porcini mushrooms - chopped; 1/2 cup dry white wine; 1 tablespoon minced fresh rosemary; 1 sheet all butter puff pastry (we used Dufour) - thawed; 1/2 pound brie - crust removed; flaked salt (we used maldon); salt and pepper; bulb onions sliced lengthwise - white and some green parts; drizzle of olive oil; melted unsalted butter (a tablesoon or so)