For the cake:
Preheat the oven to 350 degrees
Heat the 9 Tbsp. of butter in a medium saucepan over moderate heat. Cook until butter is golden brown and has a nutty fragrance. Remove from the heat and let cool for a few minutes.
Whisk together the sugar, brown sugar, and salt. Whisk in the browned butter until fully combined.
Whisk in the vanilla and eggs, one at a time.
In a separate bowl, whisk together the gluten free flour, cocoa, baking powder, and espresso powder.
Incorporate the dry ingredients into the wet ingredients.
Whisk in the warm water until fully incorporated.
Butter two 9-inch round cake pans. Cover the bottom of both pans in parchment paper rounds. Butter the top of the parchment.
Fill the pans with equal amounts of batter.
Bake in the middle rack until the cake is set and the edges begin to pull away from the pans, about 15-20 minutes.
Let cool on a wire rack. Once cooled, you can wrap them in plastic wrap and freeze. This will make it easier to frost the cakes.
For the Sugar Syrup:
In a small saucepan, heat the corn syrup, water, and sugar over medium to medium high heat. Do not stir. Insert a candy thermometer and simmer until it reaches 244 degrees. Remove from the heat.
For the meringue:
While the syrup is simmering, whisk the egg white powder, water, and salt in a standing mixer over medium high speed.
Once the syrup reaches 244 degrees, turn down the mixer to low speed. Pour in the syrup in between the whisk and bowl to keep it from sticking to the bowl. Once the syrup is incorporated, turn the speed up to medium high and whisk until you have firm peaks and the bottom of the bowl is cool to the touch, about 10-15 minutes.
Whisk in the softened butter in small pieces, a little at a time. The meringue might deflate a bit, but don't worry, keep whisking!
Turn the speed down to low and add the powdered sugar and cocoa, a little at a time, scraping down the bowl to incorporate.
Frost the cake and voila!