Preheat oven to 425° with a rack set on lowest level. Unfold pastry onto a baking sheet lined with parchment paper. In a small bowl, mix together 1 tablespoon granulated sugar, the brown sugar, cardamom, and flour. Evenly sprinkle sugar mixture over pastry.
Trim rhubarb 1 in. shorter than pastry, then split lengthwise into 1/2-in.-wide pieces. Lay pieces parallel across the pastry square, leaving 1/2 in. border of pastry. Sprinkle rhubarb with remaining 2 tablespoon granulated sugar.
Bake galette until edges are golden brown and puffed, 12 to 15 minutes. Serve with sweetened whipped cream or ice cream.
Note: Nutritional analysis is per serving.