Make the cookies: Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Beat the butter, egg yolk, vanilla, salt and cloves in a large bowl with a mixer on medium speed until creamy, about 2 minutes. Reduce the mixer speed to low; beat in the confectioners' sugar and cocoa powder until combined, then beat in the flour in two batches until combined.
Turn out the dough onto a lightly floured surface and dust with flour. Gently knead until soft but not sticky. Reflour the surface, if necessary, and roll out the dough until slightly thicker than 1/4 inch. Cut out shapes using 3-inch cookie cutters. Gently gather and reroll the scraps. (If the dough is too soft to work with, refrigerate until firm.) Arrange the cutouts about 2 inches apart on 2 unlined baking sheets.
Bake, switching the pans halfway through, until the cookies are firm, about 20 minutes. Let cool 3 minutes on the pans, then transfer to racks to cool completely.
Make the icing: Whisk the confectioners' sugar, vanilla and 1 tablespoon milk in a small bowl until smooth. Gradually stir in up to 1 more tablespoon milk until the icing is thick but pourable. Spoon the icing into a small resealable plastic bag and snip off a corner. Pipe the icing on the cookies, then sprinkle with sanding sugar. Let set, about 10 minutes.
Photograph by Ryan Dausch