Preheat oven to 350°. Line 36 mini muffin pans with paper liners.
Whisk together flour, cocoa, baking soda, and salt in a small bowl; set aside.
Beat butter and sugar until fluffy; add the eggs one at a time, beating well after each addition; then add the vanilla.
Add one third of the flour mixture, beating until smooth, then add one half of the coffee and beat well. Repeat with another third of the flour mixture and the remaining coffee, beating well after each addition; then beat in the rest of the flour mixture. Pour the batter into the cupcake liners, filling them half full. Bake about 15 minutes. Cool completely on a rack.
Meanwhile, prepare the icing. Combine the powdered sugar, milk, butter, vanilla and peppermint extracts in a medium bowl, stirring until smooth and adding a little water if needed, 1 tsp. at a time, to make a spreadable consistency. Stir in the crushed candy canes and spread about 1 tsp. of icing onto each cupcake.