Preheat oven to 375 degrees. In a small bowl, combine sugar and cinnamon. Sprinkle a work surface with 1/2 cup cinnamon-sugar mixture on it and roll out puff pastry into two 9-by-11-inch rectangles. Sprinkle each rectangle with 3 tablespoons cinnamon-sugar mixture and gently roll over dough to adhere.
Working with 1 rectangle at a time and starting from a long edge, quickly but gently fold dough toward center 3 times in 1-inch increments. Gently flip over dough and repeat with other long edge (once baked, cookies will look like an S-shape). Wrap dough in plastic and freeze until very firm but not frozen, 20 minutes.
Cut dough crosswise into 1/2-inch-thick slices. Dip both sides of each slice in remaining cinnamon-sugar mixture. In batches, place cookies, 2 inches apart, on a parchment-lined rimmed baking sheet. Bake until deep golden on underside, 12 minutes. Carefully flip each cookie with a metal spatula and bake until crisp, about 5 minutes. Transfer cookies to a wire rack set in a rimmed baking sheet and let cool completely. With a fork, drizzle cookies with chocolate and let sit until chocolate is set, about 30 minutes.
Store cookies in airtight containers, up to 1 day.