01 - Preheat oven to 350°F (180°C). Position the rack in the center.
02 - Melt butter with olive oil in a 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 pecan halves for 3 to 5 minutes until fragrant and lightly browned. Chop coarsely if desired.
05 - Place the brie wheel in a small ovenproof baking dish. For a pastry-wrapped version, lay thawed puff pastry flat, set the brie in the center, top with onions and pecans, fold the pastry over, and brush with beaten egg.
06 - Spoon the caramelized onions over the brie and scatter toasted pecans on top.
07 - Bake uncovered for 15 to 18 minutes until the cheese is soft and beginning to ooze. If using puff pastry, bake 20 to 25 minutes until the crust is deep golden brown.
08 - Let stand for 5 minutes to settle. Serve warm alongside crackers or toasted baguette slices.