In a medium size bowl, whisk together the cake flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium-high until fluffy and smooth, about 3 to 5 minutes.
Add the eggs and egg whites, one at a time to the bowl and beat on medium until well incorporated. Stir in the vanilla extract. Continue to beat on medium-high speed for about 3 minutes, until the mixture is smooth in texture and slightly bigger in volume.
Turn the mixer on low and add 1/3 of the flour mixture to the butter mixture and mix until fully incorporated. Then add half of the buttermilk, followed by another 1/3 of the flour mixture, the second half of the buttermilk and lastly, add the remaining flour mixture and mix until incorporated. Scrape down the sides of the bowl and mix on low for another 30 seconds.
Fold in the the crushed Oreos.
Evenly distribute the cake batter among the three pans, about 18 ounces in each, and bake for 35 to 40 minutes or until a toothpick inserted into the middle of the cakes comes out clean or with just a few crumbs. Make sure not to over bake.
Remove cakes from the oven and let cool in pans for 10 minutes before inverting onto cooling racks.
Once completely cooled, wrap in plastic wrap and place in the freezer or refrigerator to chill before frosting.