Make the Buttercream: Combine sugar, egg whites and salt in mixer bowl, and set over a pan of simmering water. Whisk constantly until sugar is dissolved and mixture registers 140 degrees on an instant-read thermometer.
Transfer bowl to mixer; whisk on medium-high speed until whites are fluffy and cooled, about 10 minutes. Continue to whisk until stiff, glossy peaks form.
Reduce speed to medium-low; add butter by the tablespoon, whisking well after each addition. Whisk in vanilla and peppermint extracts. Switch to the paddle attachment and continue beating until smooth. Buttercream can be refrigerated in an airtight container up to 3 days or frozen up to 1 month. Bring to room temperature before using; beat on lowest speed until smooth, about 3 minutes.
Make the Cupcakes: Preheat oven to 350 degrees. Line standard muffin tins with paper liners. Whisk together flour, cocoa powder, sugar, baking soda, baking powder, and salt. Add eggs, buttermilk, oil, water, and peppermint extract, and beat with a mixer on low speed until smooth.
Divide batter among muffin cups, filling each 2/3 full. Bake, rotating tins halfway through, until a tester inserted in the center comes out clean, 20 to 25 minutes. Let cupcakes cool in tins on wire racks for 10 minutes. Transfer cupcakes to racks, and let cool completely. Undecorated cupcakes will keep, covered, for 1 day, or frozen for up to 2 months.
Frost cupcakes with buttercream and sprinkle crushed candy on top.