Preheat the oven to 350 degrees and lightly grease a 9×13” pan.
In a saucepan over medium heat, combine the butter, coffee, and cocoa powder, stirring regularly until melted. Bring the mixture to a boil and cook for 30 seconds. Remove from heat and set aside while you assemble the dry ingredients.
In a large bowl, combine the flour, sugar, baking salt, and salt. Add the butter mixture and stir just until combined. In a small, separate bowl, whisk together the eggs, sour cream, and vanilla, and fold this mixture into the batter. Pour the batter into the prepared pan and bake until a toothpick inserted comes out clean, about 20—25 minutes.
To prepare the icing:
When the cake is about halfway through baking, combine the butter, water, cocoa powder, and vanilla in a saucepan over medium heat. Whisk regularly and be careful not to boil the mixture. Once the butter is melted, remove the pan from heat and carefully whisk in the powdered sugar until smooth. Pour the icing over the warm, finished cake and enjoy once the icing has set! Serve with a sprinkle of flaky salt if desired.