In a large bowl, whisk together the gluten free 1-to-1 baking flour, tapioca starch, 1 tablespoon sugar, and salt. Add the cold butter cubes and toss to coat. Use a pastry cutter to work the butter in, leaving some pieces about pea-sized. Drizzle in the ice water and vinegar, tossing with a fork until the dough just holds together. Shape into a rectangle, wrap in plastic, and refrigerate for 1 hour.
Mix the 1/2 cup sugar and cinnamon together. Generously sprinkle your work surface with about one-third of the cinnamon sugar. Roll the dough out on top of the cinnamon sugar into a 10x16-inch rectangle, sprinkling more cinnamon sugar over the top as you roll.
With the long side facing you, fold both long edges inward to meet at the center. Sprinkle the remaining cinnamon sugar over the top. Fold one half over the other like closing a book so you have a long, narrow, layered log. Wrap tightly in plastic and freeze for 20 minutes.
Preheat the oven to 400 F and line two baking sheets with parchment paper. Slice the chilled log crosswise into 1/3-inch-thick pieces. Place them flat on the baking sheets, spacing about 2 inches apart.
Bake for 10 minutes, then carefully flip each palmier. Bake for another 5 to 7 minutes until caramelized and deep golden. Transfer to a wire rack to cool and crisp up completely.