Preheat the oven to 400°F and line a baking sheet with parchment paper.
Place the brie wheel in the center of the thawed puff pastry sheet. Spread the fig jam evenly over the top of the brie.
Fold the pastry up and over the brie to fully enclose it, pressing edges to seal. Trim any excess pastry if needed.
Place the wrapped brie seam-side down on the prepared baking sheet. Brush the top and sides with the beaten egg.
Bake for 20 to 25 minutes until the pastry is golden brown. Remove from the oven and let rest for 5 minutes.
While the brie bakes, pour the port into a small saucepan and simmer over medium heat until reduced by half and slightly thickened, about 8 minutes. Drizzle the reduction over the baked brie before serving.