Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.
Roll out one puff pastry sheet into a large rectangle on a lightly floured surface and place on the prepared baking sheet.
Lightly score puff pastry into the shape of a Christmas tree (triangle) with a wide base. Spread chocolate-hazelnut spread over the triangle in a thin layer with the back of a spoon.
Roll out the second sheet of puff pastry to a large rectangle and place on top of the first one. Carefully trace the shape of the chocolate covered triangle underneath and cut out the Christmas tree shape and the trunk. Pull away excess pastry.
Lightly score 2 lines down the middle of the triangle to form a tree trunk that is narrower at the top and gets wider towards the base. Using the trunk as a guide, cut branches into the sides of the triangle.
Twist the branches away from you, trying to get in 2 turns on the lower branches. Continue moving up the tree, twisting away from you as you go.
Cut a small star out of the excess pastry; place on top of the tree. Brush the star and tree with beaten egg.
Bake in the preheated oven until puffy and golden brown, 12 to 15 minutes. Cool slightly, about 5 minutes. Slide onto a serving plate, using a piece of parchment paper if needed.