Make the dough: In a large bowl, whisk together flour, cocoa, baking powder, salt, and cinnamon. Set aside.
Using an electric stand mixer, beat butter and granulated sugar until light and fluffy, about 3 minutes. Beat in egg and vanilla.
With mixer on low speed, gradually add flour mixture; beat until combined.
Form dough into 3/4-inch-thick disc. Wrap in plastic; refrigerate until firm, at least 1 hour or overnight.
Roll out and freeze: Roll out dough on a lightly floured surface to 1/8-inch thickness. Cut out shapes using ring mold. Transfer shapes to a parchment-lined baking sheet. Freeze 20 minutes, until solid.
Preheat oven to 350 degrees. Bake until cookies are just set, 10 to 12 minutes.
While cookies are hot, trim to size using ring mold as guide.
Cool completely in ring molds. Transfer to freezer on a parchment-lined sheet tray.