Step 1

In a medium heatproof bowl add the chocolate, cocoa powder, and espresso powder. Pour hot water over mixture. Cover and let stand for 5 minutes. Whisk mixture gently until smooth then set aside to cool.

Step 2

Meanwhile, preheat oven to 350°F. Line a standard 12-cup muffin tin with paper liners.

Step 3

In a small bowl, whisk together the flour, sugars, salt, and baking soda.

Step 4

Whisk sour cream, oil, eggs, egg yolk, vinegar, and vanilla into the cooled chocolate mixture until smooth. Stir in the flour mixture until smooth, being careful not to overmix.

Step 5

Using a spring-loaded scoop, divide the batter evenly among prepared muffin cups until 3/4 full. Bake until cupcakes are set and firm to the touch, about 17 to 20 minutes.

Step 6

Let cupcakes cool in pan on a wire rack for 10 minutes before removing from pan to cool completely, about 1 hour. Cupcakes can be stored in an airtight container at room temperature for up to 1 day.

Step 7

In a small saucepan, bring the cream to a simmer. Remove from heat and add the chopped chocolate. Let stand for a few minutes before stirring until smooth. Set aside and cool to approximately 75°F or until thickened but still pourable.

Step 8

In the bowl of a stand mixer fitted with the paddle attachment, add the butter, powdered sugar, cocoa, vanilla, and salt. Mix on low speed until well blended and then increase the speed to medium and beat for another 3 minutes, or until very well blended, scraping down the bowl as needed.

Step 9

Reduce speed to medium-low and add the cooled chocolate cream mixture. Continue beating until the frosting has lightened in color and texture, about 2 minutes more, scraping down the bowl as needed.

Step 10

Frosting can be made 1 day ahead of time and stored in an airtight container in the refrigerator. Warm frosting in the microwave for 5 to 10 seconds and stir until creamy again before frosting cupcakes.

Step 11

Frosting can also be transferred to a ziptop bag and frozen for up to 1 month. Defrost in the fridge overnight then rewhip in the stand mixer until light and smooth.