Make the cupcakes: Preheat the oven to 325 degrees F. Line a 24-cup mini-muffin pan with paper liners. Combine the chocolate, cocoa powder and brown sugar in a large bowl; add the hot coffee and whisk until smooth. Let cool to room temperature.
Whisk the flour, granulated sugar, salt and baking soda in a medium bowl. Whisk the egg, egg yolk, vegetable oil, buttermilk and vanilla into the melted chocolate mixture. Add the flour mixture and whisk until smooth. Spoon a scant tablespoon of batter into each mini-muffin cup. Bake until a toothpick inserted into the centers comes out clean, about 15 minutes. Let cool a few minutes in the pan, then remove to a rack to cool completely.
Meanwhile, make the frosting: Combine the heavy cream, corn syrup, butter and salt in a medium saucepan and bring to a simmer. Remove from the heat; add the chocolate and whisk until smooth, then let cool to room temperature. Fill a large bowl halfway with ice water. Transfer the chocolate mixture to a medium bowl; then carefully place it in the ice water and let sit, stirring every few minutes, until the frosting is thick enough to spread, about 15 minutes.
Transfer the frosting to a pastry bag fitted with a large star tip and pipe onto the cupcakes.