Preheat the oven to 350°F.
Line a 10×15-inch sheet pan (jelly roll pan) with parchment paper, including up the sides. Spray the parchment with nonstick cooking spray. Set aside.
In a large bowl, whisk together the cake flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer with the paddle attachment, cream the butter, sugar, and vanilla extract until light and fluffy, about 5 minutes, scraping the sides of the bowl as needed.
With the mixer on the lowest speed, carefully add in egg whites, one at a time, beating well after each addition. Stop to scrape down the sides of the bowl as needed.
With the mixer still on low, add ⅓ of the flour mixture into the creamed mixture, half the milk, another third of the flour mixture, the remaining milk, and then the remaining flour mixture. Mix just until combined. Stop to scrape down the sides of the bowl as needed.
Fold in chopped Oreos™.
Pour the batter into the prepared pan. Bake for 30-32 minutes, or until a toothpick inserted in the center comes out with a few crumbs but no wet batter. Allow the cake to cool to room temperature on a wire rack before frosting with buttercream.