In a large bowl, whisk together the flour, sugar, salt, and cardamom. Using your fingertips, cut the butter into the dry ingredients until you have mostly pea-sized chunks of butter covered in flour. Using the tip of a knife, or your fingertips, stir in the vodka and apple cider vinegar until large clumps begin to form. Add in the ice water 1/2 Tbsp at a time until you can form the dough into a ball. Use your fingertips to pinch together any dry bits into the dough, sprinkle with water if needed to bring all the dough together into a ball. Shape the dough into a flat disc and wrap in plastic wrap. Chill for 30 minutes to 1 hour.