01 - Preheat oven to 350°F. Arrange a rack in the center position.
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 additional 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 until fragrant and lightly browned. Chop coarsely if desired.
05 - Place the brie wheel in a small baking dish. For a pastry-wrapped version, lay thawed puff pastry flat, set the brie on top, layer with onions and pecans, fold the pastry around the cheese, and brush the surface with beaten egg.
06 - Spoon the caramelized onions over the brie and scatter the toasted pecans on top. Bake uncovered for 15 to 18 minutes until the cheese is soft and beginning to ooze. If using pastry, bake 20 to 25 minutes until the crust is golden brown.
07 - Allow the brie to rest for 5 minutes before serving. Serve warm alongside crackers or toasted baguette slices.