In the bowl of a stand mixer combine the sugar, brown sugar, flour, cocoa powder, baking soda, baking powder and salt. Mix on low until fully combined.
In a separate bowl whisk together the egg, sour cream, milk, oil and ½ teaspoon vanilla extract.
Pour the egg mixture into the dry ingredients and beat on low until just combined.
Pour in the hot water and continue mixing until completely combined, about 1 minute.
Pour the cake batter into the prepared ramekins.
Place on a baking sheet and bake in the preheated oven for 25 - 30 minutes.
Cool the cakes completely in the ramekins on a wire rack.
Melt butter, then whisk in cocoa powder.
Add the powdered sugar, milk, and vanilla extract. Mix until spreading consistency.