In a medium saucepan, combine the butter and brown sugar. Cook over medium heat until the butter is just melted.
Remove from heat, and stir in the vanilla. Allow the mixture to stand for 15 minutes to cool slightly.
Stir in the beaten egg.
Add the flour and cocoa powder and stir until just combined.
Stir in the finely chopped pistachios.
Divide the dough in half, shape each half into a disc, then tightly wrap the discs in plastic wrap. Chill the dough in the fridge for about 30 minutes.
Pre-heat your oven to 350°F.
Take one disc and roll into out onto a lightly floured surface to about 1/4 inch thickness.
Use a tree shaped cookie cutter (or another shape if you prefer) to cut all your cookies out of the dough. Re-roll any dough scraps and continue cutting out your shapes until all the dough is used up. Repeat this process with the second half of the dough.
Place the dough cut outs onto a baking tray lined with parchment paper, spaced out 1 inch apart.
Bake for 8-10 minutes until the edges start to firm.
Allow the cookies to cool on the tray for 5 minutes, before transferring them to a wire rack to cool completely.