01 - Preheat oven to 350°F. Position the rack in the center.
02 - Heat butter and olive oil in a large skillet over medium-low heat. Add the thinly sliced onions and cook for 15 to 20 minutes, stirring frequently, until deeply golden and very soft.
03 - Stir in brown sugar, thyme leaves, salt, and pepper. Continue cooking for 2 to 3 minutes until the onions are fully caramelized and glossy. Remove from heat and set aside.
04 - In a dry skillet over medium heat, toast the pecans for 3 to 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. If using puff pastry, lay the thawed pastry sheet flat, set the brie in the center, and proceed to the next step before wrapping.
06 - Spoon the caramelized onions over the top of the brie and scatter the toasted pecans on top. If wrapping with puff pastry, fold the pastry over the brie, seal the edges, and brush the surface with beaten egg.
07 - Bake uncovered for 15 to 18 minutes until the cheese is soft and beginning to ooze. If wrapped in puff pastry, bake 20 to 25 minutes until the pastry is golden brown and puffed.
08 - Let the brie stand for 5 minutes to settle. Serve warm alongside crackers or toasted baguette slices.