Fig and Balsamic Syrup Mille Feuille

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1 sheet puff pastry, thawed, if frozen (1/2 (17 1/4-ounce) package)

All-purpose flour, for dusting

1 large egg white, beaten

3 tablespoons plus 1 teaspoon granulated sugar, divided

1/4 teaspoon ground cinnamon

1/2 cup balsamic vinegar

1/2 cup Ruby Port wine

1/2 vanilla bean, split lengthwise in 1/2, seeds scraped

2 cups black Mission figs, stems removed and cut in 1/2 vertically

1 cup heavy cream

1 teaspoon pure vanilla extract

4 teaspoons confectioners' sugar