Preheat the oven to 350 degrees F. Spray a 9x13-inch baking pan with non-stick cooking spray, set aside.
In a medium-sized bowl, mix the flour, baking powder, salt, and baking soda, set aside.
In the body of a stand mixer with the paddle attachment or in a large bowl with an electric hand mixer, cream the butter with the sugar for 2 minutes until light and fluffy, scrape down the sides as needed.
Add the egg whites into the mixer in three batches, mixing them in fully before the next addition.
Slowly stir in the milk and vanilla until smooth.
Add half of the flour mixture and mix in until combined.
Mix in half of the sour cream until combined. Repeat with the remaining flour and sour cream.
Scrape down the sides and stir in the chopped Oreos.
Pour the batter into the baking dish and smooth out the top.
Place in the oven and bake for 35-42 minutes until a toothpick inserted into the center comes out clean.
Remove from the oven and place on a wire rack to cool completely.
While the cake is cooling, make the frosting by placing the butter into a large bowl with an electric hand mixer and beat until smooth.