Preheat the oven to 350°F. Line a standard 12-cup muffin pan with liners. Set aside.
Add the butter and chocolate to a microwave-safe bowl. Heat in 20-second increments, stirring after every 20 seconds, until the chocolate is melted and smooth (about 1-2 minutes total). Set aside to cool slightly.
In the bowl of a stand mixer fitted with the whisk attachment, add the eggs, sugar, vanilla, and sour cream. Whisk on medium speed until smooth. (about 1 minute)
In a separate bowl, whisk together the cocoa powder, flour, baking soda, baking powder, and salt.
Add the butter and chocolate mixture to the stand mixer and whisk for about 30 seconds, or until smooth.
With the mixer on low, slowly sprinkle in the flour mixture, about ¼ cup at a time. Mix until just combined. The batter will be very thick.
Fill the cupcake liners ⅔ of the way full with batter. Bake for 15-18 minutes. The center of the cupcake should spring back up if gently pressed, and a toothpick should come out mostly clean when inserted in the middle. Allow the cupcakes to cool.