Combine the butter, sugar and cheese in the bowl of a stand mixer fitted with a paddle attachment. Beat until smooth and creamy, about 2 minutes. Do not incorporate too much air by raising the speed. Beat in the egg until incorporated.
In a separate bowl, whisk together the flour, baking powder, salt and cayenne to combine. Mix in the pistachios and cranberries.
On low speed, add the flour mixture to the creamed butter-cheese mixture in a few additions, scraping the bowl and beater in between.
Spread the dough along the edge of a large piece of waxed paper or plastic wrap. Using the edges of the paper or plastic, roll the dough into a log shape about 12 inches long. Twist the ends to close. Refrigerate for a minimum of 1 hour or freeze up to four weeks.
Preheat the oven to 350 degrees F.
Unwrap the dough log and, using a sharp knife, slice into 1/4-inch thick rounds. Place the rounds on parchment-lined or nonstick baking sheets and bake for 10 to 12 minutes, or until lightly golden brown. Remove to a rack to cool completely. Store in an airtight container for up to one week.