Preheat oven to 350 degrees F. Lightly coat twelve 2-1/2-inch muffin cups with nonstick cooking spray; set aside. In a medium bowl, stir together flour, cocoa powder, baking powder, salt, and baking soda; set aside.
In a very large bowl, beat shortening with an electric mixer on medium to high speed for 30 seconds. Add the 1/2 cup sugar and the vanilla. Beat until combined, scraping side of bowl occasionally. Add egg yolks one at a time, beating well after each addition. Alternately add flour mixture and water to shortening mixture, beating on low speed after each addition just until combined.
Thoroughly wash beaters. In a large bowl, beat egg whites on medium speed until soft peaks form (tips curl). Gradually add the 1/3 cup sugar, 1 tablespoon at a time, beating on high speed until stiff peaks form (tips stand straight). Fold one-fourth of the beaten egg whites into chocolate batter to lighten. Gently fold in the remaining beaten egg whites. Gently fold in chocolate pieces. Divide among the prepared muffin cups.
Bake for 20 to 22 minutes or until a toothpick inserted near the centers comes out clean. Cool in pan on a wire rack for 5 minutes. Remove cupcakes from pan; cool completely on wire rack.
Up to 4 hours before serving, prepare Creamy Peppermint Frosting. Cut cupcakes in half horizontally. Spoon about 1 tablespoon of the frosting onto the bottom of each cupcake. Replace cupcake tops, pressing gently to spread frosting to edges.
Place the 1/4 cup crushed candies on a sheet of waxed paper. Roll sides of cupcakes in crushed candies to coat the exposed frosting. Pipe or spread the remaining frosting onto tops of cupcakes. If desired, sprinkle with additional crushed peppermint candies. Makes 12 cupcakes.
Creamy Peppermint Frosting
Allow butter to stand at room temperature for 30 minutes. In a large mixing bowl beat butter, marshmallow creme, and peppermint extract with an electric mixer on medium speed until smooth. Gradually add 2 cups of the powdered sugar, beating well. Beat in the 2 tablespoons milk. Gradually beat in the remaining powdered sugar. If necessary, beat in additional milk, 1 teaspoon at a time, until frosting reaches spreading consistency.