01 - Preheat your oven to 350°F. Position the rack in the center of the oven for even heat distribution.
02 - Heat the butter and olive oil in a skillet over medium-low heat. Add the thinly sliced onions and cook for 15 to 20 minutes, stirring frequently, until they turn a deep golden color and become very soft.
03 - Stir in the brown sugar, fresh thyme leaves, salt, and black pepper. Continue cooking for an additional 2 to 3 minutes until the onions are fully caramelized and glossy. Remove the skillet from heat and set aside.
04 - In a dry pan over medium heat, toast the pecan halves for 3 to 5 minutes until fragrant and lightly browned. Chop coarsely if desired, then remove from heat.
05 - Place the brie wheel in a small baking dish. For a wrapped version, lay the brie on the thawed puff pastry sheet, top with the caramelized onions and toasted pecans, fold the pastry around the cheese, and brush the surface with the beaten egg wash.
06 - Spoon the caramelized onions over the brie wheel and scatter the toasted pecans evenly across the top.
07 - Bake the brie for 15 to 18 minutes until the cheese is soft and beginning to ooze. If using the puff pastry wrapper, bake for 20 to 25 minutes until the pastry turns a deep golden brown.
08 - Allow the baked brie to rest for 5 minutes before serving. Present warm alongside crackers or toasted baguette slices.