Preheat oven to 350°F (175°C). Grease two 8- or 9-inch round pans with baking spray (with flour) or use shortening and flour.
In a large bowl, combine cake mix, egg whites, vanilla, sour cream, heavy cream, and crushed Oreos.
Mix everything together until well combined and smooth, about 2 minutes at medium speed.
Divide batter between the prepared pans.
Bake for about 22–23 minutes, or until cakes are set and a toothpick comes out clean.
Let cakes cool in pans briefly, then remove and wrap in plastic until ready to frost.