Combine the butter and sugar in a saucepan; heat and stir until butter is melted and mixture is smooth. Remove the pan from heat and stir in the vanilla. Cool for 15 minutes.
Whisk in the egg, flour and cocoa, then the ¾ cup of pistachios. Cover and chill for 30 minutes, or until easy to handle.
Preheat the oven to 350℉. On a floured surface, roll the dough to ¼ inch thickness. Cut into 2-inch hearts, trees or any other symmetrical shape. Bake on an ungreased cookie sheet until firm, about 9 minutes. Cool.
Melt the chocolate and shortening in a small pan (or Pyrex container in microwave) and stir until smooth. Dip half of each heart in mixture. Edge with ground pistachios. Place the dipped cookies on waxed paper until the chocolate sets completely. Store in a covered container with sheets of waxed paper dividing layers (they also freeze well).
Notes
When melting chocolate and shortening in microwave, cook for 30 seconds, take out and stir, cook a little more, stir until nice and smooth for dipping.
Almonds may be substituted for the pistachios, if you'd like.