In a medium heavy-bottomed saucepan over medium-high heat, combine the butter, water and cocoa powder. Stir often, until the butter is melted, then bring the mixture to a boil. Remove from the heat and let cool for 15-20 minutes.

In a large bowl, whisk together the gluten-free flour, granulated sugar, brown sugar, baking soda and salt.

In a medium bowl, whisk together the sour cream, eggs and vanilla. Add the sour cream mixture to the dry ingredients and stir until well-combined.

Once the butter-cocoa mixture has cooled for at least 15 minutes, pour it into the batter and whisk until smooth.

Pour the batter into the prepared pan. Bake for 20-24 minutes, until the edges pull away from the sides of the pan and a toothpick inserted into the center of the cake comes out clean.

Once the cake has finished baking (or several minutes before), begin preparing frosting.

In a medium heavy-bottomed saucepan over medium-low heat, add the butter and milk. Stir until the butter is melted. Remove from the heat and whisk in the powdered sugar, cocoa powder and vanilla until completely smooth.

Pour the frosting over the warm cake. Use an offset spatula to spread the frosting into an even layer. Allow frosting to set for about 10 minutes before slicing.