Preheat oven to 350 degrees. Line standard muffin tins with paper liners. Whisk together cocoa and hot water until smooth. In another bowl, whisk together flour, baking soda, baking powder, and salt.
Melt butter with sugar in a saucepan over medium-low heat, stirring to combine. Remove from heat, and pour into a mixing bowl. With an electric mixer on medium-low speed, beat until mixture is cooled, 4 to 5 minutes. Add eggs, one at a time, beating until each is incorporated, scraping down sides of bowl as needed. Add vanilla, then cocoa mixture, and beat until combined. Reduce speed to low. Add flour mixture in two batches, alternating with the sour cream, and beating until just combined after each.
Divide batter evenly among lined cups, filling each three-
quarters full. Bake, rotating tins halfway through, until a cake tester inserted in centers comes out clean, about 20 minutes. Transfer tins to wire racks to cool 15 minutes; turn out cupcakes onto racks and let cool completely. Cupcakes can be stored overnight at room temperature, or frozen up to 2 months, in airtight containers.
To finish, use a small offset spatula to spread cupcakes with frosting.
Refrigerate up to 3 days in airtight containers; bring to room temperature and garnish with chocolate curls just before serving.