Preheat oven to 400° F. In a medium skillet, melt butter over medium heat.
Add figs and walnuts and sauté for one minute. Add Port and nutmeg and cook for 2 minutes, stirring occasionally. Add sugar, cook for one minute, remove from heat and cool slightly. Add 2 Tbsp. beaten egg and combine well.
On floured parchment paper, lay piecrust flat. Cut the Brie in half horizontally. Place the bottom layer of Brie in the center of the piecrust and top with half the fig and walnut mixture. Replace top of Brie and layer on the remaining filling.
Pull piecrust up and over the sides of Brie, leaving the filling exposed.
Brush crust with remaining egg wash. Bake for 15-18 minutes until crust is golden brown. Cool 10 minutes before serving in wedges.
