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.
Meanwhile, preheat the oven to 350°F. Line a standard 12-cup muffin tin with foil or paper liners.
In a small bowl, whisk together the flour, sugar, salt, and baking soda.
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.
Using a spring-loaded scoop, divide the batter evenly among prepared muffin cups. Bake until cupcakes are set and firm to the touch, about 20 minutes. 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.
Combine the sugar, egg whites, and salt in the bowl of a stand mixer. Set bowl over a saucepan filled with 1-inch of gently simmering water. Whisking gently and constantly, heat mixture until sugar is dissolved and mixture is slightly thickened and foamy and registers 150°F on a candy thermometer or a digital thermometer, about 3 minutes.
Fit stand mixer with whisk attachment and beat the egg white mixture on medium speed until slightly cooled and thickened, about 2 minutes. Add the butter, 1 piece at a time, until smooth and creamy. If the mixture looks curdled, that’s okay. Just keep beating until it becomes smooth.
Add chocolate and vanilla and mix until combined. Increase speed to medium-high and beat until light, fluffy, and well combined, about 30 seconds, scraping down the sides of the bowl as necessary.
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.
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.