Preheat oven to 400 degrees F.
Remove 1 sheet of puff pastry sheet from freezer. Thaw according to package directions.
On a floured surface, roll the puff pastry out, so the creases disappear. It should increase in size at least 1 inch all around.
Using a dinner plate, cut out a large circle. Refrigerate trimmed pieces.
Trim or scrape the rind off the brie round on one side only.
Place the brie in the middle of the puff pastry circle, scraped side up.
Top brie with fig spread and walnuts.
Put 1 egg and 1 teaspoon water in a small bowl. Whisk to combine.
To wrap the brie, carefully bring the puff pastry up and over one side of the round.
Using the egg/water mixture to seal the folds, continue to fold the pastry over the brie, going in a circle.
Gently push the folds together when finished.
Carefully transfer wrapped brie to a baking sheet.
Remove trimmed pieces of puff pastry from refrigerator. Use a glass or round cutter to make a 3 or 4 inch circle. Cover the top of the wrapped puff pastry with the circle. Using tiny shaped cutters, use the pastry to decorate the top of the brie.
Brush the entire round of pastry with egg mixture.
Bake in center of oven for 35-40 minutes. Pastry should be golden and puffed.
Cool 10 minutes before serving.
Garnish with fresh thyme if desired. Serve with crackers, apple slices, red grapes, flat pretzels, or baguette slices.