Sift together flour, cocoa powder, cinnamon, and salt. Beat butter and confectioners' sugar with a mixer on medium-high speed until pale and fluffy. Beat in egg and vanilla. Reduce speed to low. Gradually add flour mixture, and beat until just combined. Divide dough in half, and shape into disks. Wrap each disk in plastic, and refrigerate until firm, at least 1 hour (or up to overnight).
Preheat oven to 350 degrees. On a lightly floured piece of parchment (or between 2 pieces of parchment), roll the dough to 1/8 inch thick. Transfer the dough and parchment to a baking sheet. Freeze 15 minutes.
Using a 2 1/2-by-3-inch fluted oval cookie cutter, quickly cut out shapes. (If dough begins to soften, place in freezer for 3 to 5 minutes.) Gather scraps, reroll, and cut out. Space shapes 2 inches apart on parchment-lined baking sheets. Freeze 15 minutes.
Brush flour from shapes. Bake, rotating sheet halfway through, until crisp, 8 to 10 minutes. Let cool completely on sheets on wire racks. (Undecorated cookies can be stored in airtight containers for up to 1 week.) Just before serving, decorate cookies: Center template over cookie. Lightly sift confectioners' sugar over template, then carefully lift it off cookie. Repeat with remaining cookies.