What a cute cake! I can’t wait to make this one. Completely iced cakes are always so pretty, but there’s something about cramming all that wonderful icing between the layers that is enticing.
Combine sugar and egg whites in a mixer bowl. Whisk together over simmering water until hot to the touch, and until all the sugar has melted and is no longer grainy.
Transfer bowl to mixer stand and whip on high until fluffy and cool (about 10 minutes).
With the mixer on low, add the softened butter one tablespoon at a time until incorporated. Add vanilla. Beat until smooth. (The mixture may appear curdled, but continue to mix and it will become smooth.)
Divide the frosting into three bowls. In one of the bowls, stir in the melted bittersweet chocolate to make the chocolate frosting. In another bowl, add the strawberries and 1 tablespoon sugar to a blender; puree. Strain through a fine mesh strainer to remove the seeds. Stir 1/2 cup of puree into the frosting. If you prefer a deeper red, add a few drops of red food coloring.
Trim the cake layers with a sharp, serrated knife so they’re as flat as possible. Freeze the layers for 15 minutes.
Top the first layer with chocolate frosting and smooth with an offset spatula. Leave a 1-inch border around the outside.
Add another layer and repeat with the vanilla frosting. Add the final layer upside down and top with strawberry frosting.
Using a large star tip, pipe the borders of the cake with the corresponding frosting. Top with chocolate sprinkles.