Preheat oven to 180°C (350°F). Grease, line with parchment, and flour two round 20cm (8-inch) pans.
In a medium bowl or measuring cup, combine and stir the egg whites, 1/4 cup of milk, and the vanilla. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, combine the dry ingredients together on low speed for 30 seconds. Add the butter and remaining 1/2 cup of milk, and mix on low speed until just combined. Increase to medium speed and mix for 1 1/2 minutes.
Scrape the sides of the bowl and begin to add the egg mixture in 3 separate batches; beat on medium speed for 20 seconds after each addition.
Divide the batter in two into the prepared cake tins, spreading it evenly with a small offset palette knife. If you have a kitchen scale, weigh to ensure 2 even layers.
Bake 25-35 minutes, but be careful to not overbake. Check cakes at 20 minutes, but not before, and once you feel it’s almost ready, set the timer for 2 minute intervals. They’re cooked when they turn light golden yellow, spring back when lightly pressed, and when an inserted toothpick comes out clean.
Let cakes cool on racks for 10 minutes before loosening the sides with a small metal spatula, and invert onto wire racks. Gently turn cakes back up, so the tops are up and cool completely.
When cooled, you can trim the tops of the cakes to create a flatter surface, however I left them as they were. Place one cake onto a serving platter and spread some of the icing over top with a palette knife. Put the second cake on top and spread more icing on top, then use the remaining icing to spread around the sides. Decorate as you please.