1. Preheat oven to 350°F (177°C). Prepare three 8-inch round cake pans with parchment and grease. Alternatively, use a 9×13-inch pan or two pans for a two-layer cake.
2. Whisk together flour, sugar, baking powder, and salt.
3. Add softened butter one tablespoon at a time until the mixture resembles coarse crumbs.
4. Mix in oil, then stir in sour cream and vanilla, followed by milk.
5. Whip egg whites until stiff peaks form, then gently fold into the batter.
6. Carefully fold in broken Oreo pieces.
7. Divide batter evenly into prepared pans and bake for 30-35 minutes or until lightly touching the top springs back or a toothpick comes out clean.
8. Cool cakes in the pans for 15 minutes, then invert onto racks to cool completely.

Cream Cheese Frosting:
1. Beat butter and cream cheese until creamy.
2. Gradually add powdered sugar, salt, and vanilla, then beat in heavy cream if using until smooth and light.
3. Use about two-thirds of the frosting between cake layers and on the top, pressing crushed Oreo crumbs halfway up the sides. Mix some crumbs into remaining frosting for piping.