While the method itself offers endless possibilities, I really love this combination of earthy mushrooms, sweet caramelized onions and rich gooey cheese. It's a wonderful shareable appetizer, or even a meal if you really, really like cheese. (I do.)
The method for stuffing and cooking the brie comes from a recipe at FoodWishes.com, and the caramelized onion technique is Mark Bittman's. The filling combination and other instructions are my own.
Read more on my blog: https://whateverpieces.wordpress.com/2015/12/21/caramelized-onion-and-mushroom-stuffed-baked-brie/ —Stephanie H.
Unwrap the puff pastry and place it on a plate on the counter to thaw. This should take 30-40 minutes. Meanwhile, place the Brie in the freezer to chill it well.
Heat a lidded skillet over medium heat. When hot, add the onions and cover. Cook, stirring occasionally, until the onions soften and begin to brown and stick to the pan. Remove the lid and add 1 tbsp butter, a pinch of salt and a grind of pepper. Continue to cook, uncovered, stirring occasionally, until caramelized. Remove to a bowl to cool.
In the same skillet, melt the remaining 1 tbsp butter. Add the mushrooms, garlic and thyme, and cook until the mushrooms brown, stirring occasionally. When the mushrooms begin to release liquid, add the soy sauce, vinegar, and vermouth or wine. Continue to cook until the liquid evaporates and the mushrooms appear glazed. Taste and add pepper and salt (if necessary). Remove to a separate bowl to cool.
Preheat the oven to 425F. (If desired, spread baguette slices on a baking sheet and toast them in the oven for a few minutes.) Line a baking sheet with a piece of parchment paper.
Remove the Brie from the freezer. Using a sharp knife, score the equator of the wheel, making a cut about 1/8– to ¼-inch deep all the way around. Work a piece of kitchen twine or plain dental floss into the cut, tying the ends together in an overhand knot. Pull the ends in opposite directions (as if you were tightening the knot) to cut through the cheese. Pull the two halves apart.
Unfold the puff pastry on the baking sheet. Place one half of the Brie (rind-side down) on the pastry. Layer the mushrooms and then the onions on top of the cheese. Top with the other half of the Brie, rind-side up.
Brush the puff pastry with the beaten egg. Then, pull the pastry up over the cheese and pinch together the edges to seal it in completely. It’s ok if you need to stretch it a little, or cut off some extra. Flip the Brie over so that it is seam-side down, and brush the outside with the beaten egg. You can decorate the top with extra puff pastry before brushing with the egg, if desired.
Bake the Brie 20-25 minutes until the pastry is golden brown on the outside. The cheese will probably ooze a bit—that’s ok! Let it rest just a minute or two before removing to a cutting board or platter. Serve with toasted bread or crackers.