Preheat the oven to 275 degrees F. Grease and flour an 8 ½ x 4 ½ inch loaf pan or grease, line with parchment and grease again. I tend to do the latter because I am paranoid about cake sticking to the loaf pan.
In a 3-quart saucepan, begin melting the butter over medium low heat. Add the chopped chocolate and stir well, then pour in the coffee. Stir until melted and smooth, then remove from heat and let cool for a few minutes before adding the egg.
Whisk in the egg and vanilla.
Mix together the flour, sugar, baking powder, salt and cocoa powder. Add the dry ingredients to the chocolate mixture and whisk until well combined and smooth. Pour batter into the loaf pan.
Bake at 275 degrees F for 45 to 50 minutes or until a cake tester comes out clean. You’ll know the cake is done when a crack appears on the top. Allow the cake to cool in the pan for 15 minutes, then turn out onto a cooling rack to finish cooling.
Sour Cream Chocolate Frosting: In large mixing bowl, beat the butter until creamy. Add the sugar and the cocoa powder and mix well, then stir in the sour cream. Begin mixing with the electric mixer until everything holds together. Beat in the vanilla. Add a pinch of salt and continue beating until smooth and creamy, adding whole milk until the icing is a spreading consistency. It should be very smooth.