Generously dust your work surface with sugar. Place the dough in the center and sprinkle the top with one cup sugar (if making savory palmiers, add the savory ingredient just before you fold into the heart shape), covering it completely. Roll into a 16 by 10-inch rectangle, using additional sugar as needed to keep the dough from sticking to the surface.
Make a book fold (four layers). Using a ruler and the back of a knife, mark a line dividing the dough in half length-wise, each half measuring 8 x 10 inches. Using the ruler and knife again, mark each half into quarters. Fold the two short edges to the quarter mark and fold over again until you are 1/4 of an inch away from the center (do this on both sides). Tighten each side to leave 1/4 inch space down the center of the dough. Fold one side on top of the other, forming a 10-inch long cylinder.
If you look at the end of the cylinder, you’ll see the shape of a heart. Wrap in plastic and refrigerate for 30 minutes.
Line the baking sheets with parchment paper or silicone mats. Preheat oven to 375 degrees and position an over rack in the center. Place the remaining sugar in a small mixing bowl. Trim the ends of the cylinder if they are uneven or cracked, then cut twelve 1/4-inch thick slices from the chilled cylinder, dip each side in sugar, and place two inches apart on the baking sheet. (Any left over dough that is not going into the oven, rewrap and return to the refrigerator.)
Bake the cookies for 7-10 minutes, or until golden at the edges. With a spatula, flip each cookie over. Return to the over and bake for 9-12 minutes longer, until they are a beautiful golden brown (or bake for a total of 20 minutes, checking at 10 minutes, but with no need to flip - they will still look and taste delicious). Transfer to a rack and cool completely.
OPTIONAL: Freeze any of the palmier dough and book folds before slicing if you don't need to bake them all at this time. I wrap mine in plastic wrap, label - savory or sweet), and place in the freezer for up to 6 months. When I know I will be baking them, I take them out 4-8 hours ahead of time by placing in the refrigerator (not leaving them on the counter as you want the dough to be chilled so that it puffs!). Then follow the instructions for baking as shared above. If you don't have any time to defrost in the refrigerator, slice gently (some pieces may fall apart - that is okay as they will bake back to together), then top with the cheese or sugar before placing in the oven for two-three additional minutes beyond 20 minutes.