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Heat the oven to 200C/180C fan/gas 6. Unroll the two pastry sheets, keeping them on their baking parchment. Spread the pesto over one of the pastry sheets, then scatter over half of the grated cheese. Flip the second sheet of pastry on top and press to stick the two pastry sheets together. Remove the top layer of parchment.
Cut out a Christmas tree shape – a large triangle with a little stump at the bottom, using as much of the pastry as possible. Cut a star shape out of the offcuts for the top of the tree. Reserve the rest of the offcuts. Lift the tree onto a large baking tray, brush with the beaten egg, then do the same with the star and press it on the tip. Scatter over the rest of the cheese and gently press to help it stick to the pastry.
Cut vertical lines into the sides of the tree, about 1cm apart, leaving a ‘trunk’ of about 2cm up the middle. Twist the strips of pastry and stick them back down to the tray. Do this with all the pastry ‘branches’. Cut the offcuts into straws, and arrange them on another baking tray. You can now wrap and chill the tree and offcuts for up to two days, freeze for two months, or bake straightaway.