Preheat oven to 450°F and place an oven rack in the center. Line a baking sheet with a Silpat.
Unfold or gently roll the thawed puff pastry to an even square. Cut the square into 4 equal smaller squares and place them on the Silpat-lined baking sheet, spacing them apart.
In a small bowl, beat the large egg with 2 tablespoons water until combined; set the egg wash aside.
In another bowl, mix 1/2 cup Nutella and 1/4 cup peanut butter until smooth.
Divide the Nutella–peanut butter mixture into four equal portions. Spoon one portion onto the center of each pastry square, leaving about a 1/2-inch border around the edges.
Place four banana slices on top of the filling on each square. Lightly sprinkle cinnamon sugar over the banana slices.
Lightly brush the pastry borders with the egg wash, fold each square diagonally to form a triangle, and press the edges together firmly with a fork to seal.
Brush the tops of the sealed turnovers with more egg wash, sprinkle a little more cinnamon sugar on top if desired, and cut a small vent hole in the top of each turnover.
Bake on the center rack for about 15 minutes, until the turnovers are puffed and golden brown.
Remove from the oven and let the turnovers rest a few minutes before serving, as the filling will be very hot.