Preheat the oven to 350ºF. Line a baking sheet with parchment paper or a Silpat.
In the bowl of a stand mixer fitted with the paddle attachment, cream together butter and sugar. Once light and fluffy, add the flour. Mix until a soft dough forms, then turn out onto a lightly floured surface. Roll the dough out to ¼ inch thickness, then use a cookie cutter to cut into rounds. Using a sharp, clean knife, slice each circle in half. Place cookies on the prepared baking sheet and bake 16-17 minutes or until the edges just begin to brown. Allow the cookies to cool on the pan for two minutes before removing to a wire rack to cool completely.
While the cookies are cooling, melt the chocolate over a double boiler. Meanwhile, finely chop pistachios or place them in a food processor and pulse until finely ground (but not powdery). Transfer the nuts to a bowl and mix in cayenne pepper.
Dip cooled cookies a little over halfway in chocolate, allowing any excess to drip off. Then dip the top side of the chocolate cookie into the nuts. Place cookies on parchment paper to allow the chocolate to set.