1Process butter in a food processor until smooth. Add granulated sugar and brown sugar and process until thoroughly blended into butter, about 1 minute. Add egg yolks and vanilla; process until mixture is smooth and looks glossy, about 30 seconds. Add salt, cinnamon, ginger, cardamom, baking powder, and 2 cups plus 2 Tbsp. flour; pulse until dough comes together around the blade. Turn out onto a work surface and knead a couple of times to incorporate any floury bits. Divide dough in half; pat into two ½"-thick disks. Wrap in plastic and chill until firm, 45–60 minutes.
2Let dough sit 5 minutes at room temperature to soften slightly.
3Preheat oven to 350°. Working with 1 disk at a time, roll out dough on a lightly floured surface to ¼" thick. Punch out cookies with cookie cutters and transfer to parchment-lined baking sheets, spacing at least 1" apart. Sprinkle with sanding sugar, if using, and press in lightly to adhere. Gather up scraps and reroll once. Chill cookies on baking sheets until firm, 5–10 minutes, then bake until edges are golden brown, 12–18 minutes. Let cool 5 minutes on baking sheet; transfer to a wire rack and let cool completely.
4Do Ahead: Dough can be made 1 month ahead; freeze instead of chilling.