Combine brown sugar and cardamom in a small bowl. Unfold dough flat on a work surface and sprinkle evenly with half the sugar mixture.
Using a rolling pin, lightly roll sugar into dough so that most of sugar sticks, being careful not to change the shape of the dough. Turn pastry over and sprinkle evenly with remaining sugar.
Beginning with the side closest to you, fold in dough, 1 in. at a time, to the center of the rectangle. Repeat with the opposite side. Fold one half on top of other as if closing a book. Wrap dough airtight and chill at least 1 hour.
Preheat oven to 400°. Using a sharp knife, cut dough into 1/2-in. slices. Line 2 baking sheets with parchment paper and lay slices on flat sides about 2 in. apart. Bake slices until doubled in size and golden, about 10 minutes. Let cookies cool completely on trays.
Make ahead: Unbaked palmiers can be frozen up to 2 weeks; baked palmiers may be made up to 2 days ahead and kept airtight at room temperature.
Note: Nutritional analysis is per palmier.