Preheat the oven to 350℉ and grease a square 8x8-inch pan or one 9-inch round pan. Line with parchment paper to prevent sticking.
In a medium mixing bowl, use an electric hand mixer or stand mixer to cream together the butter and sugar. Set aside.
In a large mixing bowl, whisk flour and baking powder to combine.
To another large mixing bowl, add the egg whites. Using an electric hand mixer or stand mixer, whip the whites on high speed until light and fluffy, about 2 minutes.
Add the butter/sugar mixture to the flour and baking powder mixture. Mix on low speed to combine. Stir in the milk and vanilla extract and mix again until all ingredients are well incorporated.
Using a silicone spatula, fold in the egg whites until just combined.
Pour mixture into the greased baking pan and bake in preheated oven for 30 minutes or until a toothpick comes out clean when inserted in the center of the cake.
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Notes
Be sure to grease the cake pan and line it with parchment. Unlike a layer cake, this type of cake is typically served directly from the pan.
If the batter seems dry, stir in a teaspoon of milk at a time until there are no dry clumps of flour.
To prevent a dense cake, whip the egg whites well.