Rotate adding the milk and dry ingredients to the wet ingredients until the cake batter is combined. Mix at medium-high speed and scrape down the sides of the bowl as needed.
Toss a cup of chocolate chips in the reserved flour, then fold it into the batter.
Divide batter equally between the pans and bake for 30-35 minutes. Once done, cool the cakes on a wire rack for 20 minutes. Then remove from the pan and continue cooling. While the cake is baking, start making the frosting.
Cream butter and add the powdered sugar half at a time on low speed, working up to high speed. Beat until the buttercream is fluffy. Add the vanilla, and continue mixing for 2 minutes.