How to Make It
In a medium bowl, whisk the flour with the salt, ginger, cardamom and black pepper. In a large bowl, using a hand mixer, beat the butter with the confectioner’s sugar at medium speed until light and fluffy, about 3 minutes. At low speed, beat in the dry ingredients until only a few streaks of flour remain. Using a rubber spatula, fold in the candied ginger. (The dough will be crumbly.)
Transfer the dough to a large sheet of plastic wrap and pat into a rectangle about 1/2 inch thick. Wrap tightly and freeze until firm, about 20 minutes.
Preheat the oven to 325°. Unwrap the dough and place between 2 sheets of parchment paper. Roll out the dough 1/8 inch thick and slide onto a rimmed baking sheet; freeze until firm, about 10 minutes.
Remove the top sheet of parchment and slide the chilled dough onto a work surface. Line 2 rimmed baking sheets with parchment. Using a 2-inch star cookie cutter (or other cookie cutters as desired), cut out about 30 cookies, rerolling the scraps once. Arrange the cookies on the prepared baking sheets about 1 1/2 inches apart.
Sprinkle the dough with the turbinado sugar and bake for 20 to 22 minutes, until the shortbread are lightly golden brown around the edges. Transfer the cookies to a wire rack and let cool completely.