1. Chocolate Glaze: Whisk to combine confectioners' sugar and cocoa in a bowl. Stir in milk, and whisk until smooth.

2. Cookies: Whisk to combine flour, cocoa powder, salt, and cinnamon in a bowl. In a separate bowl, beat butter and confectioners' sugar with an electric mixer on medium-high speed until pale and fluffy, 3 to 4 minutes. Mix in egg and vanilla. Reduce speed to low. Gradually mix in flour mixture. Divide dough in half; wrap each in plastic, and chill 1 hour or up to 1 day.

3. Roll out dough between 2 sheets of parchment to 1/8-inch thickness. Transfer to a baking sheet. Chill 15 minutes.

4. Preheat oven to 350 degrees. Using a 5-inch moose-shaped cookie cutter, quickly cut out shapes from dough (if dough begins to soften, chill 5 minutes more). Reroll scraps and cut out more shapes. Transfer shapes to parchment-lined baking sheets, spacing 2 inches apart. Chill 30 minutes.

5. Bake, rotating sheets halfway through, until cookies are crisp, about 8 minutes. Let cool completely on sheets on wire racks.

6. With an offset spatula, spread glaze on cookies. Allow glaze to set for 30 minutes before serving. Glazed cookies can be stored between layers of parchment in an airtight container at room temperature up to 3 days.