Prep: If frozen, let pastry thaw on the counter until soft and pliable. Once thawed, cut into 8 equal squares. Preheat oven to 400°F (204°C). Slice the onion and remove thyme leaves from stems.
Layer: Line a large baking sheet with parchment paper. Drizzle oil equally around the baking sheet to make 8 little puddles. Drizzle on balsamic. Top each with an onion slice. Sprinkle on thyme leaves, salt, and pepper. Top with a slice of brie.
Cover: Top each mound with the puff pastry, pressing the edges down to completely cover the cheese and onion. Whisk the egg together then brush it over the pastry.
Bake: Bake on the middle rack for 15 minutes, or until golden brown and cooked through. Let cool on the baking sheet for a few minutes before trying to remove from the parchment.
