Preheat oven to 375°F. Butter a small, 6-cup Bundt, 6-inch round, or 8-inch square or round baking pan, and dust with flour (or use baking spray). Melt butter and set aside to cool. Whisk together the flour, baking powder, and salt and set aside.
Using an electric mixer with whisk attachment, beat egg whites until foamy, sprinkle in the cream of tartar, and continue to beat until they are glossy and hold firm peaks. Set aside or transfer to another bowl.
Using whisk or paddle attachment, beat egg yolks, sugar, cooled melted butter, and vanilla until thick and pale yellow. Sprinkle in the flour and mix just until combined.
Using a rubber spatula, fold ¼ of the egg whites into the batter. Gently fold in the remainder of the whipped egg whites, scoop into prepared pan, and smooth the surface. Optionally sprinkle brown sugar on top.
Bake for 35–40 minutes until top is beginning to turn golden brown (start checking at 30–35 minutes for 8-inch pans). Let cool 10 minutes in pan then, if using Bundt pan or if desired for rounds, invert onto cooling rack. Square cake can remain in the pan. Keep loosely covered to preserve the crust. Enjoy!