Preheat the Oven: Preheat your oven to 425°F (220°C).
Prepare the Puff Pastry: Lay the thawed puff pastry flat on a parchment-lined baking sheet. Place the wheel of brie in the center of the pastry. Score the top of the brie in a crosshatch pattern using a knife.
Add the Toppings: Spread fig preserves evenly over the top of the brie. Drizzle with honey and sprinkle fresh thyme leaves and a pinch of black pepper for extra flavor.
Wrap with Prosciutto: Gently wrap the slices of prosciutto around the brie. Fold the corners of the puff pastry up and over the brie, sealing the edges to completely encase the cheese.
Brush and Sprinkle: Brush the puff pastry with the beaten egg to give it a golden finish. Lightly sprinkle coarse sugar on top for a hint of sweetness and extra crunch.
Bake: Bake in the preheated oven for 20-25 minutes, or until the puff pastry is golden brown and crispy.
Serve: Serve warm with your favorite bread or crackers for dipping.