First, brown your butter. Melt butter in a saucepan and continue to cook on medium-low, watching carefully for bubbles to subside and the bottom of the liquid to begin browning. Once it is taking on a golden brown color, remove from heat. It should smell nutty and have little brown bits in it.
Pour in a small bowl and allow to cool back to room temperature. It should be soft and spreadable.
Preheat oven to 350° F. Spray two 6" cake pans and line bottoms with parchment paper rounds.
In a small bowl, combine milk, egg whites, and vanilla.
In the bowl of a stand mixer fitted with the paddle attachment, combine dry ingredients until thoroughly combined. Add soft brown butter, blending until mixture looks like breadcrumbs.
Add all but 1/4 cup of milk mix and beat on medium speed until thick and creamy, 2-3 minutes. With mixer on low, gradually pour in remaining milk.
Divide batter evenly between the prepared pans and use a spatula to even out.
Bake until golden brown on top and sides are beginning to pull away from the pan, about 25-30 minutes. Allow to cool completely.