Preheat your oven to 350°F. Grease a 9x5 inch loaf pan and line the bottom with parchment paper (leaving a bit of overhang to make it easier to pull the cake out). Set aside.
Make the chocolate loaf cake: In a medium bowl, combine flour, cocoa powder, baking powder, baking soda, and salt. Whisk to combine and set aside. In a large bowl, combine butter and granulated sugar. Using an electric mixer fitted with the beater attachment or a wooden spoon by hand, cream together until the sugar is dissolved and the mixture lightens in color (about 2 minutes on medium speed or 5 minutes by hand).
Add your eggs in, one at a time, beating well after each addition. Mix in your vanilla extract.
Alternate adding in your dry ingredients and sour cream to the butter mix. Mix in about half of the dry mix, followed by all of the sour cream. Finish off with the remaining dry ingredients, and mix together until just combined.
Pour the pound cake batter into your prepared loaf pan, and spread into an even layer. Bake in the center of your preheated 350°F oven for 45 to 55 minutes, or until a skewer inserted into the center comes out clean. If the cake starts browning too quickly, loosely tent the top with aluminum foil, and continue baking until cooked through.
Cool your cake in the pan for about 20 minutes, then pull out using the parchment overhang and transfer onto a wire rack. Set aside to cool completely to room temperature before icing.
Make the cocoa powder icing: In a medium sized bowl, combine powdered sugar, cocoa powder, and 2 tablespoons of milk / heavy cream. Whisk to combine. If your icing is too thick, gradually whisk in more milk or heavy cream, 1 tablespoon at a time, until it reaches your desired consistency.
Drizzle your chocolate icing over the cooled pound cake. Slice and serve!