Preheat the oven to 350°F (175°C). Grease and line two 8-inch cake pans with parchment paper.
In a large bowl, whisk together the flour, baking powder, and salt.
In another bowl, cream together the sugar, vegetable shortening, and butter until light and fluffy.
Mix in the egg whites one at a time, followed by the sour cream and vanilla extract.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the chopped Oreos.
Divide the batter evenly between the prepared pans and bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes before transferring to a wire rack to cool completely.