In a medium-size bowl, whisk together flour, cinnamon, and salt.
In the bowl of a standing or electric mixer, cream butter, sugar, and zest until light and fluffy.
Reduce speed to low and gradually add flour mixture until dough comes together in clumps.
Add pistachios and cranberries.
Gather and press dough together. Cut dough in half and place each half on a sheet of waxed paper.
Form each half into a log about 1-½ inches in diameter. Square off each log to form a bar (pressing two rulers along the length of the dough is helpful), and wrap each bar in waxed paper.
Chill until very firm, at least 2 hours.
Adjust oven rack to middle position and preheat to 350°. Meanwhile, line two large baking sheets with parchment paper.
In a small bowl, beat egg. Brush egg over logs on all sides.
Place coarse sugar on a separate sheet of waxed paper. Roll bars in sugar, coating well.
Cut each bar crosswise into ¼-inch-thick slices, rotating bar after cutting each slice to keep square shape. (If dough is too soft to slice, freeze briefly until firm.)
Arrange cookies about a half inch apart on lined baking sheets. Bake 15–18 minutes.
Transfer cookies from parchment to racks and cool completely before serving.