Place sugar and orange zest in food processor. Process for 1 minute.
Add cardamom, salt, orange juice, and cranberries. Pulse several times, until cranberries start turning into small bits.
Then add flour. Process until well combined, about 30 seconds.
Cut butter into ~1/4" slices and sprinkle over top of flour mixture. Process again until a soft dough forms.
Remove dough from processor and form into a large cylinder, about 3 inches in width and 15 inches in diameter. Cover in plastic wrap and place in refrigerator for at least 4 hours.
Preheat oven to 350 degrees. Line cookie sheet with parchment paper or silicone baking mats.
Cut dough into ~1/4" slices. Bake for 9-10 minutes, or until tops start to turn golden. Let cool on sheet for at least 3 minutes before removing to cooling rack.