1. Sift together flour, cocoa, salt, and cinnamon into a bowl. With an electric mixer, beat butter and confectioners' sugar on medium-high speed until pale and fluffy, about 3 minutes. Mix in egg and vanilla. Reduce speed to low. Gradually mix in flour mixture. Wrap dough in plastic wrap. Chill 1 hour.

2. Preheat oven to 350 degrees. On a lightly floured work surface, roll out dough to 1/8 inch thick. Transfer to a parchment-lined baking sheet. Freeze 15 minutes.

3. Using a 2- or 3-inch X- or O-shaped cookie cutter, quickly cut out shapes from dough (if dough begins to soften, return to freezer for 3 to 5 minutes). Reroll scraps once and cut out more shapes.

4. Transfer shapes to baking sheets, spacing them 2 inches apart. Freeze until firm, about 15 minutes. Brush flour from shapes. Sprinkle with sanding sugar. Bake until crisp, rotating sheets halfway through, about 8 minutes. Let cool completely on sheets on wire racks. Cookies can be stored in an airtight container at room temperature for up to 1 week.