Preheat oven to 180C (360F) fan forced. Line 2 baking trays with baking paper.
Use a food processor to finely grind the pistachios. Reserve 125g (1 ¼ cups) for the dough and 75g (¾ cup) for decorating.
In a medium saucepan, melt the butter and brown sugar over a medium-low heat, stirring continuously until smooth and the sugar is mostly dissolved. Remove from the heat and stir in the vanilla. Cool for 10 minutes.
Add the egg to the cooled butter mixture, followed by the ground pistachios, then the cocoa powder and flour, stirring after each addition until the mixture forms a smooth dough.
Divide the dough into two portions, cover, and refrigerate for 30 minutes.
Roll out the dough to a thickness of 5mm then refrigerate for 30 minutes. Use a Christmas tree cookie cutter to cut shapes.
Bake the biscuits for 5 minutes until the edges are firm. Allow the biscuits to cool completely before decorating.
Melt the chocolate in the microwave then stir in the oil. Dip one side of each biscuit into the chocolate mixture, and then dip the coated edge in the remaining ground pistachios. Allow the chocolate to set before serving.