Preheat the oven to 350F (180C) degrees. Line the bottom of two 8-inch cake pans with parchment paper, and grease and flour the sides.
Whisk together the flour, baking powder and salt in a medium bowl.
In a liquid measuring cup, whisk together the milk, oil and peppermint extract.
In a large bowl, beat the butter and sugar until fluffy (about 3 minutes).
Mix in the egg whites about 1-2 at a time, turning off the mixer and scraping down the sides of the bowl as necessary.
Sift in about ⅓ of the flour mixture (do not just dump it in, otherwise there will be lumps). Mix on a low speed until combined.
Then mix in about ½ of the milk. Repeat the process, sifting in about ⅓ more of the dry ingredients and mixing in, followed by the rest of the milk. Finally, sift in the rest of the dry ingredients and mix in until just combined.
Pour the batter evenly between the 2 pans. Bake both cakes in the middle of the oven for about 25-30 minutes, or until an inserted toothpick comes out clean and the sides of the cake are starting to pull away from the edges of the pan.
Cool the cakes in the pans for at least 1 hour, then gently invert the cake pans and remove the cakes from the pans. Continue cooling.