In a medium saucepan, melt the butter. Whisk in the sugar and cocoa powder. In a separate bowl, whisk together the cream and the sour cream. Slowly add this to the pan, whisking it in until well combined and smooth. Mix in the espresso powder and heat until the sugar has dissolved. Remove from heat and stir in the vanilla.
Let the icing sit at room temperature until it is a good consistency for icing your cake or cupcakes. To speed up the process, place it in the refrigerator. Keep an eye on it and take it out when it firms up enough to ice. If it gets too firm, you can always stick it in the microwave for a few seconds to soften it up again.
Notes
*this recipe will make enough frosting for a two-layer cake, and MAYBE enough for a 3-layer cake. It will also be enough to frost about 36 cupcakes.