Spread ½ cup of sugar over a countertop or cutting board. Unfold pastry and place on top of sugar. Using a drinking glass or rolling pin, roll the puff pastry out to a 13- x 13-inch square, pressing the sugar into the dough.
Thinly spread either Bittersweet Chocolate and Sea Salt Halva Spread or the Vanilla Bean Halva Spread on top of the dough. Roll one side tightly to the middle. Then roll the other side tightly to the middle, so both rolls meet in the middle.
Wrap with plastic wrap and freeze for 30 minutes. Repeat the procedure with the other sheet of dough.
Preheat oven to 400°F. Line 2 baking sheets with parchment paper.
Using a sharp knife, slice the dough into ¼-inch slices. Place slices 1½ inches apart on a baking sheet.
Bake at 400°F for 12 to 15 minutes or until the bottom and sides of the cookies are caramelized. Remove from parchment and transfer to a rack or plate to cool.