Cover the puff pastry with a slightly damp kitchen cloth and bring to room temperature.
Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper and set aside.
On a lightly floured surface, roll out the pastry to 1/8-inch thickness. Using a 3-inch round cutter dipped in flour, press out into 8 portions. Place on the prepared baking sheet. Brush the pastry with the egg white. Combine 1 teaspoon of the granulated sugar with the cinnamon and sprinkle evenly over the pastry. Cover with a sheet of parchment paper and top with a second baking sheet.
Bake until lightly browned and cooked through, about 30 minutes. Remove from the oven and transfer to a wire rack to cool completely.
Combine the vinegar, Port, 1 tablespoon of granulated sugar and the vanilla bean and seeds into a small saucepan. Bring to a boil. Reduce the heat to medium-low and cook until the mixture is thick and syrupy, 12 to 15 minutes. Add the figs, turning to coat evenly, and cook for 1 minute. Remove from the heat and cool slightly. Discard the vanilla bean pods.
Beat the cream in a medium bowl until soft peaks form. Add the remaining 2 tablespoons of granulated sugar and the vanilla extract, and beat until stiff peaks form.
To assemble, place a small dollop of whipped cream in the center of each of 4 plates. Top with 1 pastry round and a dollop of whipped cream. Divide the figs evenly among the rounds, reserving 4 halves for garnish. Top with the remaining pastry rounds and whipped cream, and garnish with the fig halves. Dust with confectioners' sugar and serve.