Preheat oven to 350F . Line 3 8" pans or 4 6" pans with parchment paper and grease the sides.
Whisk the milk , egg whites and vanilla extract and set aside.
In a bowl of a standing mixer, place the flour,espresso powder sugar,salt and baking powder. Using the paddle attachment, mix on low to combine.
Increase speed to medium and add the butter one piece at a time until the mixture is moist and crumbly.
Add half a cup of the liquid mixture into the mixer bowl, once the liquid is in incorporated let it mix for about 1 minute.
Add the remaining of the liquid mixture. Mix just to combine.
Divide the batter between the pans and bake in the middle rack for 18-20 minutes for ,or until a toothpick comes out clean from the center of the cake.