Preheat oven to 350°. Line a 9” round cake pan with foil and spray with nonstick cooking spray. You can also use a springform pan (grease it with cooking spray, no foil needed).
Whisk flour, sugar, cocoa, salt, and baking soda in a large bowl. Add egg, oil, buttermilk, white vinegar, and vanilla to a large measuring cup or extra bowl and whisk until combined. Add to dry ingredients and mix with a hand mixer until smooth. Add red food coloring and mix slowly until combined.
Pour batter into the prepared cake pan.
Make the cheesecake: Mix cream cheese, sugar, vanilla, egg and sour cream with a hand mixer until smooth. Stir in Oreo chunks. Spread carefully over cake batter in pan.
Bake about 30-40 minutes or until a toothpick stuck in the cake part comes out clean. The cream cheese filling will be the teeniest bit jiggly still. Cool to room temperature, then chill for at least 2 hours before frosting.
Make the frosting: Using a hand or a stand mixer, cream butter and cream cheese until fluffy, then mix in the cocoa. Slowly add in powdered sugar, salt, and vanilla. Mix until smooth. The frosting should be spreadable without milk, but if it seems too thick, add up to 1 tablespoon of milk, 1 teaspoon at a time. Optionally add more crushed Oreos to the frosting.
Frost around the edges of the cake and top with Oreo cookie halves.