01 - Preheat oven to 350°F. Position a rack in the center of the oven.
02 - Melt butter with olive oil in a large skillet over medium-low heat. Add the thinly sliced onions and cook for 15–20 minutes, stirring frequently, until deeply golden and very soft.
03 - Stir in brown sugar, thyme leaves, salt, and pepper. Continue cooking for 2–3 additional minutes until the onions are fully caramelized and glossy. Remove from heat and set aside.
04 - In a separate dry skillet over medium heat, toast the pecans for 3–5 minutes, tossing occasionally, until fragrant and lightly browned. Chop coarsely if desired.
05 - Place the Brie wheel in a small oven-safe baking dish. For a pastry-wrapped version, lay the Brie on a sheet of thawed puff pastry, top with onions and pecans, fold the pastry around the cheese, and brush with beaten egg.
06 - Spoon the caramelized onions over the top of the Brie and scatter the toasted pecans over the onions. Bake uncovered for 15–18 minutes, until the cheese is soft and beginning to ooze. If using puff pastry, bake 20–25 minutes until the crust is golden brown.
07 - Allow the baked Brie to rest for 5 minutes before serving. Serve warm alongside crackers or toasted baguette slices.