Place mashed bananas in a medium bowl. Pour in brown sugar and vanilla. Mix together until well incorporated. Set aside.
Unfold 1 pastry sheet on a lightly floured surface. Cut the sheet in half lengthwise. Using a rolling pin, roll out each piece into a 15×5 inch rectangle. Cut each rectangle crosswise to make 3 5-inch squares. Repeat with the remaining pastry sheet. This will make 12 squares total.
Spoon 1-2 tablespoons of the banana mixture into the center of each square. Fold each corner into the center over the filling, and sealing by pinching the pastry dough together.
Place the filled pastries onto a parchment lined baking sheet. Brush each pastry bundle with milk.
Stir the cinnamon and sugar together in a small bowl. Sprinkle mixture over each bundle.
Bake in a preheated oven for 15 minutes until the pastries are golden brown. Remove from the baking sheet and let cool on a wire rack until ready to serve.