Add the butter and chocolate to a large, heatproof bowl. Bring 1-2 inches of water to a simmer in a medium saucepan. Turn the heat down to low and set the bowl on top. Stir together with a spatula until the chocolate and butter have melted together and are smooth, then remove the bowl from the heat.
Once combined, pour into a large bowl and whisk in the cocoa powder and vanilla extract (Note: you can also use an electric mixer for the following steps). Whisk in about half of the sugar and sour cream. The frosting will be very thick at this point.
Keep whisking in additional sugar and sour cream until the desired texture and flavor is reached. I typically add most of the sour cream and not all of the sugar.
This frosting will keep in an airtight container in the refrigerator for 1 week. It can be frozen for up to 3 months. Allow it to come to room temperature before using, and use a whisk, electric mixer, or stand mixer to fluff it back up prior to using.
Yields approximately 2 to 2 1/2 cups total (it will vary slightly depending on how much sour cream and sugar you use). That's enough for approximately 15-18 cupcakes or one sheet cake. I recommend doubling the recipe if you want to use it for a layer cake.