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1
Preheat oven to 350F.
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2
Line standard muffin tins with paper liners.
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3
Whisk together cocoa and hot water until smooth.
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4
In another bowl, whisk together flour, baking soda, baking powder, and salt.
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5
Melt butter with sugar in a saucepan over medium-low heat, stirring to combine.
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6
Remove from heat, and pour into a mixing bowl.
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7
With an electric mixer on medium-low speed, beat until mixture is cooled, 4 to 5 minutes.
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8
Add eggs, one at a time, beating until each is incorporated, scraping down sides of bowl as needed.
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9
Add vanilla, then cocoa mixture, and beat until combined.
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10
Reduce speed to low.
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11
Add flour mixture in two batches, alternating with the sour cream, and beating until just combined after each.
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12
Divide batter evenly among lined cups, filling each three-quarters full.
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13
Bake, rotating tins halfway through, until a cake tester inserted in centers comes out clean, about 20 minutes.
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14
Transfer tins to wire racks to cool 15 minutes; turn out cupcakes onto racks and let cool completely.
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15
Cupcakes can be stored overnight at room temperature, or frozen up to 2 months, in airtight containers.
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16
To finish, use a small offset spatula to spread cupcakes with frosting.
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17
Refrigerate up to 3 days in airtight containers; bring to room temperature and garnish with chocolate curls just before serving.
