1. Preheat oven to 350°F (177°C). Prepare three 8-inch round cake pans by lining bottoms with parchment and greasing sides.
2. In a large bowl, whisk flour, sugar, baking powder, and salt.
3. Add softened butter gradually, mixing on low speed until mixture resembles coarse, sandy crumbs.
4. Stir in oil, then sour cream and vanilla extract, mixing on low until combined.
5. Add milk and combine on low speed without overmixing.
6. In a separate clean bowl, beat egg whites with an electric mixer until stiff peaks form.
7. Gently fold whipped egg whites into batter using a spatula to maintain lightness.
8. Fold in broken Oreo pieces, preserving chunks.
9. Evenly distribute batter into prepared pans and bake 30-35 minutes until a toothpick comes out clean or with moist crumbs.
10. Cool cakes in pans 15 minutes, then transfer to racks to cool completely.

For the Frosting:
1. Beat butter and cream cheese on medium speed until smooth.
2. Gradually add powdered sugar on low speed, scraping bowl as needed.
3. Add salt, vanilla, and optionally heavy cream for desired consistency.
4. Beat on high speed 15-30 seconds until light and fluffy.
5. Reserve two-thirds for frosting the cake.
6. Press pulverized Oreo crumbs halfway up frosted cake sides by hand.
7. Mix 3-4 tablespoons Oreo crumbs into reserved frosting and pipe swirls on top using a piping bag with large tip.