Prepare the Cake: Preheat your oven to 350°F (177°C) and generously grease a 9×13-inch baking pan to prevent sticking.
In a medium bowl, whisk together the cake flour, baking powder, baking soda, and salt. Set this dry mixture aside. Using either a hand mixer or a stand mixer fitted with the whisk attachment, beat the softened butter on high speed until smooth and creamy, about 1 minute. Add the granulated sugar and continue beating on high speed for another 2 minutes until the mixture is well creamed. Use a rubber spatula to scrape down the sides and bottom of the bowl as needed. Add in the egg whites and beat on high speed until fully incorporated, about 2 minutes. Next, add the sour cream and vanilla extract, beating until combined. The mixture may look slightly curdled at this stage, which is normal. With the mixer on low speed, gradually add the dry ingredients until just combined. While still mixing on low, slowly pour in the milk until everything is blended—do not overmix. Finish by whisking the batter gently by hand to ensure there are no dry patches or lumps at the bottom of the bowl. Gently fold in the chopped Oreo cookies, being careful not to overmix the batter.
Pour the cake batter into the prepared pan and smooth it out evenly. Bake for 32 to 35 minutes, or until a toothpick inserted into the center comes out clean. Once baked, remove the cake from the oven and allow it to cool completely in the pan on a wire rack. Make sure the cake is fully cooled before applying the frosting.
Prepare the Whipped Cream Frosting: In a large mixing bowl, use a hand mixer or stand mixer fitted with the whisk attachment to beat the softened cream cheese on medium-high speed until creamy, about 1 minute. Scrape down the sides and bottom of the bowl and continue beating if needed to ensure a smooth consistency. Add in the confectioners’ sugar and vanilla extract, and beat on medium speed for about 2 minutes until the mixture is fully combined and smooth. Scrape the bowl again. With the mixer running on low speed, slowly pour in the cold heavy cream in a steady stream. Once all the cream has been added, increase the mixer speed to high and beat until the frosting becomes thick and stiff peaks form, usually about 1 to 2 minutes.
Frost the Cake: If you plan to do decorative piping, set aside about 1 cup of the whipped cream frosting before adding the chopped Oreos. Fold the chopped Oreo cookies into the remaining frosting (or all of it, if not piping). Spread the frosting evenly over the cooled cake—it will be a thick, fluffy layer. A small offset spatula works especially well for spreading frosting on a 9×13-inch sheet cake. For piped decorations like the pictured zigzag border, use a Wilton 1M piping tip or similar to pipe around the edges.
Serving and Storage: You can serve the cake right away or cover it and leave it at room temperature for a few hours before serving. Alternatively, refrigerate the frosted cake for up to 1 day and allow it to come to room temperature before serving for the best texture and flavor. Though it can also be served chilled, many prefer the frosting softer at room temperature. The frosting holds up well at room temperature or even in warmer environments for several hours. Store any leftover cake tightly covered in the refrigerator for up to 5 days.