Using an electric mixer, cream the butter and sugar together until light and fluffy—3-5 minutes. (Don’t skimp on the time–this make a big difference in texture.)
Add the vanilla and salt and mix in. Then slowly add the flour until just combined. Mix in the chocolate and pistachios.
Dump the dough onto a large piece of plastic wrap. Press into a disk, then wrap well. Refrigerate for at least 30 minutes before rolling.
Preheat the oven to 350 degrees F and line your cookie sheets with parchment paper. Break the dough in half, leaving half in the fridge.
Flour a work surface and roll out half the dough until 1/4-inch thick. Using a 2- to 3-inch cookie cutter, cut out the cookies very close together. Then gather the remaining dough, re-roll and cut again. Every time you roll out the dough it gets tougher, so try to cut as many from the first roll as possible. Repeat with the remaining dough.
Bake for 15-20 minutes and cool on the cookie sheets 2-3 minutes, before moving to a cooling rack.