Line a baking tray with aluminium foil and grease with the coconut oil.
Cut puff pastry in half; roll into two 33x40cm / 13-16in sheets on a lightly floured surface.
Place 1 puff pastry sheet on the prepared baking sheet. Lightly score puff pastry into the shape of a triangle with a wide base.
Spread room-temperature chocolate-hazelnut spread over the triangle in a thin layer with the back of a spoon.
Roll up the second sheet of puff pastry and place on the tip of the triangle; roll down to cover the chocolate spread. Score top puff pastry sheet into a triangle; cut out carefully to avoid tearing aluminum foil. Pull away excess pastry.
Cut away 2 strips at the bottom of the triangle to form the base of a tree trunk. 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.