Remove the dough from the refrigerator and square off the dough by pressing the round edge on the counter four times. If necessary, let the dough sit at room temperature until pliable enough to roll. Mix the sugar with the cardamom. Transfer 1 tablespoon of the sugar mixture to a small cup and mix in the salt. Set aside.
Sprinkle the work surface liberally with some of the remaining cardamom sugar. Set the dough on the sugared surface and sprinkle it with more of the sugar. Turn the dough frequently and resugar it and the work surface liberally as you roll the dough into a 24x8-inch rectangle that's less than 1/8 inch thick. Use the sugar generously to prevent sticking and to ensure that the cookies will caramelize properly in the oven. Trim the edges of the rectangle evenly.
Mark the center of the dough with a small indentation. Starting at one short edge, fold about 2-1/2 inches of dough almost one-third of the distance to the center mark. Without stretching or pulling, loosely fold the dough over two more times, leaving a scant 1/4-inch space at the center mark. Likewise, fold the other end of the dough toward the center three times, leaving a tiny space at the center. The dough should now resemble a long, narrow open book. Fold one side of the dough over the other side, as if closing the book. You should have an eight-layer strip of dough about 2-1/2 inches wide and 8 inches long.
After folding in both sides of the palmier dough three times, you should have a 1/4-inch gap between the two sides, Then fold one side over the other, as if closing a book.
Sprinkle the remaining cardamom sugar under and on top of the dough. Roll gently from one end of the dough to the other to compress the layers and lengthen the strip to about 9 inches. Wrap the dough loosely in waxed paper (not plastic wrap, which might cause moisture to form on the outside of the dough and dissolve the sugar). Refrigerate the dough for at least 30 minutes or up to 4 hours.
Position racks in the upper and lower thirds of the oven and heat the oven to 375°F. Remove the dough from the refrigerator, unwrap it, and use a sharp knife to trim the ends evenly. Cut 1/3-inch slices (I mark the dough at 1-inch intervals and cut three slices from each inch) and arrange them 1-1/2 inches apart on two ungreased or foil-lined cookie sheets. Bake until the under-sides are golden brown, 8 to 10 minutes, rotating the pans from top to bottom and front to back about halfway through baking.
Remove the pans from the oven and turn the cookies over. Sprinkle each one with a pinch or two of the reserved salted sugar mixture. Return the sheets to the oven until the cookies are deep golden brown, another 3 to 5 minutes. Rotate the pans and watch the cookies carefully at this stage to prevent burning. If the cookies brown at different rates, remove the dark ones and let the lighter ones continue to bake. Transfer the cookies to a rack and let cool completely. Store airtight.