Preheat the oven to 350°F (180°C). Grease a 9-inch cake pan or springform pan. If using a cake pan, line the bottom with parchment paper strips in an X shape, then place a parchment round at the bottom.
In a stand mixer or using a hand mixer, cream the butter, light brown sugar, and granulated sugar until fluffy, about 3 minutes.
Add the eggs and egg yolk one at a time, mixing after each addition and scraping down the sides of the bowl. Stir in the vanilla extract.
Gradually add the flour, baking soda, and sea salt. Once almost combined, fold in the chopped Oreos.
Spread the cookie dough evenly into the prepared pan with an offset spatula. Bake for 22-30 minutes, or until golden brown and a toothpick inserted in the center comes out clean.
Allow the cake to cool completely on a wire rack before removing it from the pan.
While the cake cools, prepare the frosting by creaming the butter and powdered sugar together. Add the heavy cream, vanilla extract, and a pinch of sea salt. Beat on medium speed until light and fluffy.
Once the cake has cooled, use a pastry bag with a star tip to pipe the vanilla frosting on top. Garnish with sprinkles or additional chopped Oreos. Serve and enjoy!