Put a medium saucepan on the stove over high heat.
Put the figs, honey, and water in the pan, stir, and bring to a boil. Reduce heat, and allow the water to simmer. The honey and natural sugars from the figs should thicken the water. Continue to simmer figs until a sauce is achieved that is thick enough to cover the back of a spoon. When sauce has reached that consistency, remove from heat. Put "fig sauce" in a refrigerator-safe container, and allow cooling for at least 20 minutes.
Spread a sheet of puff pastry out on a clean, lightly floured surface. Scoop a small amount of fig sauce on the puff pastry sheet with about 2 inches around the sauce on every side. Put a piece of Brie on top of the sauce. Carefully fold the edges of the puff pastry over the cheese. Squeeze the edges of the pastry together then carefully flip the pastry over, so the smooth surface of the pastry is facing up. Gently take the pastry and put it on a sheet tray lined with parchment paper. Repeat this until all the cheese is used. You should have 8 small stuffed pastries.
When all the pastries are on the sheet tray, take a pastry brush, and lightly brush egg whites on the top and sides of each pastry, this will give the pastry a shine when it comes out of the oven.
Drizzle a small amount of honey on top of each pastry.
Bake the pastries until the puff pastry is a golden brown. This should take about 15 minutes, but keep your eyes on the baking process. When the pastries are golden brown, remove from the oven, and allow them to cool on a cooling rack. Allow them to cool for 3-5 minutes, then serve warm.
