To make the buttercream: Create a double broiler using the bowl of a stand mixer placed over a large pot filled with about 2 inches of water. Allow the water to come to a boil before starting the frosting.
In the bowl of the stand mixer placed over the pot in the double broiler, combine the brown sugar and egg whites. Whisking constantly, continue to heat the mixture for approximately 3-5 minutes.
Switch the whisk attachment for a paddle attachment. While the mixer is going on low/medium speed, add the vanilla and slowly add in cubes of butter, mixing well between each addition.