1. Program the oven to 350F and let it heat up, then line a baking sheet with parchment paper.
2. Place a pot over high heat and add water, then pour the figs and two teaspoons of honey into it, and boil. Lower the heat and let the water simmer, till it thickens from the natural sugars to form a sauce. Then, turn the sauce into a container and chill for 20 minutes in the fridge.
3. Dust the counter surface with flour and spread a sheet of puff pastry on top, then spread a bit of the sauce on it, letting the sheet about two inches around the sauce.
4. Place a piece of the cheese on the sauce, fold the sheet edges over the cheese, and squeeze the edges together to hold. Then, gently flip the pastry to face the smooth side up and transfer it to the lined baking sheet. Repeat the process for the rest of the sheets and ingredients to make a total of eight stuffed pastries.
5. Brush the top and sides of the pastries with the egg whites and drizzle the rest of the honey on each piece. Then, bake the pastries for 15 minutes or until they develop a golden brown look.
6. Take the baked pastries out and let them cool for three to five minutes, then serve warm.

You can also follow this video recipe for more assistance.