Heat oven to 375°F. Line three baking sheets with parchment. Dip a 1½-inch round cookie cutter in extra cocoa and tap onto parchment to create a cookie outline; repeat to make outlines 1 inch apart on all the baking sheets' set aside. Whisk together cocoa, flour, baking soda and salt; set aside.

In a mixing bowl beat together the butter, shortening and sugars until smooth, about 2 min. Add egg and vanilla and beat until fluffy, 2 min. Stir in half the flour mixture, then the milk, and beat to combine. Add remaining flour mixture and beat together, scraping down sides of bowl.

Transfer batter to a piping bag fitted with a coupler or a ½-inch plain tip. Pipe onto parchment, filling the outlines with mounds about ½ inch high. Bake, one sheet at a time, until cookies spring back to the touch, 10 to 12 min. Cool on baking sheets 10 min, then transfer to a wire rack with a metal spatula and let cool completely.

Spread about 1 tablespoon buttercream on flat sides of half the cookies and sandwich with remaining cookies. Cover edges with sprinkles. Can be made up to 1 day ahead and stored chilled. Bring to room temperature before serving.