Heat oven to 350° F.
Grease, flour and line cake pans with parchment paper.
In mixing bowl, sift together the flour, cocoa powder and baking powder.
To the flour mixture, whisk in the brown sugar and salt until combined.
In a small bowl, add the milk and the white vinegar; set aside.
In bowl of stand mixer with whisk attachment (or using a hand mixer), beat together the eggs and oil until frothy, about 3 minutes. Add vanilla extract.
Add the milk mixture to the egg mixture and beat gently until combined.
With a spatula, gently *fold* (resist the urge to use the mixer) the dry ingredients into the egg/oil mixture until all traces of the flour have been incorporated.
Divide batter equally and pour into both pans.
Bake for about 20 minutes or until toothpick comes out clean when inserted in the center of each cake. Note: Rotate pans at the midway point for a more even bake. Allow cake to cool completely before frosting.