Preheat oven to 350°F. Line two baking sheets with parchment paper. Set aside.
Following package directions, beat butter in a mixing bowl with an electric mixer. Add the dry sugar cookie mix, cardamom, and dried or fresh orange peel to the bowl. Mix on low speed until crumbly. Add egg and beat on low speed until dough comes together. This will take a few minutes, but be patient, it will come together nicely. Remove dough from beaters. Scrape down sides of bowl with a large spatula and push the dough together into a ball.
Lay a large rectangle piece of parchment paper out onto a clean, flat surface. Transfer the dough to the parchment paper. Using your hands, form the dough into a thick rectangle. Tear off another sheet of parchment paper and place on top of the dough. Roll the dough out into a large rectangle that is about 10- by 15- inches and ¼-inch thick. Trim the sides and patch as needed to make the dough as rectangular as possible.
Sprinkle the chopped figs and pistachios evenly over the dough, leaving a bit of a margin around the edges. Gently press the figs and nuts into the dough.
Gently fold one of the long edges (about 1-inch) over onto itself. Use the parchment to lift the rest of the dough and roll it over. Be sure to roll as tightly as you can. When you reach the end, gently press the dough onto itself to seal it.
The dough can be chilled or cut into cookies right away.
Use a very sharp knife to cut 30, ½-inch thick rounds. Place on the parchment lined baking sheets. Gently use the palm of your hand to press the cookies down, especially if any of them have gaps or holes.
Bake for 12-15 minutes, or until golden brown and firm. Let cool on baking sheets. Transfer to an airtight container. Will keep for about 1 week at room temperature. For longer storage, freeze in an airtight container with waxed paper between the layers.