Preheat the oven to 400°F.
Roll out the thawed puff pastry on a lightly floured surface to smooth out any creases.
Place the Brie cheese in the center of the puff pastry. Spread the fig jam evenly over the top of the Brie.
Sprinkle the chopped prosciutto over the fig jam. Drizzle honey on top of the prosciutto.
Fold the edges of the puff pastry over the Brie, pinching to seal it completely. Trim any excess pastry if necessary.
Brush the top of the pastry with the beaten egg to give it a golden color when baked.
Place the wrapped Brie on a baking sheet lined with parchment paper.
Bake in the preheated oven for 25-30 minutes, or until the pastry is golden brown and puffed.
Remove from the oven and let it cool for about 5 minutes before serving. Garnish with fresh thyme leaves if desired.