Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.

In a medium bowl, combine the chopped figs, walnuts, melted butter, brown sugar, orange zest, cinnamon, and nutmeg. Mix until the ingredients stick together slightly.

Roll out the puff pastry on a lightly floured surface to about 1/4 inch thickness.

Using a 4-inch round cutter or a small bowl, cut out 8 circles from the pastry.

Place a generous tablespoon of the fig mixture into the center of each pastry circle, leaving a border around the edge.

Lightly brush the edges with water, then gather the dough edges up over the filling and pinch them together tightly to seal.

Turn the cakes over so the seam is at the bottom. Gently flatten each cake with a rolling pin until it is about 3 inches wide, ensuring the fruit doesn't break through.

Make three small parallel cuts across the top of each cake with a sharp knife to allow steam to escape.

Brush the tops with the beaten egg and sprinkle generously with demerara sugar.

Bake for 15-20 minutes, or until the pastry is puffed and deep golden brown. Let them cool on a wire rack before serving.