Line a baking sheet with a Silpat mat. Parchment is fine, but the caramel can stick to it more than a silpat.
Cut out both puff pastry sheets in the shape of a Christmas tree on the countertop including the trunk. Evenly spread Nutella on one sheet of pastry.On the other sheet spread the dulce de leche. Flip the nutella side onto the dulce de leche.
Transfer to baking sheet. Cut slits on both sides spacing them about 1-inch apart without cutting into the center.
Twist each strip of pastry twice, pressing the ends onto the baking sheet to help them to stay down. Cut out two star shapes with the leftover pastry, spread one with Nutella and the other with dulce de leche and put the two pieces together. Place the star on the top of the tree.
Brush pastry with egg yolk mixed with the water. Bake for 25-30 minutes at 400°F (200°C) until golden.
1 Egg Yolk, 1 teaspoon Water
Allow to cool for 5 minutes. Lightly brush pastry with the melted butter (you may not use it all), and sprinkle with cinnamon sugar. Serve immediately.