1. Mix the chocolate cookie crumbs with melted butter until the mixture resembles wet sand. Press this mixture evenly into the bottom of a 9-inch springform pan.

2. Bake in a preheated oven at 350°F (175°C) for 10 minutes, then allow to cool completely.

3. Preheat the oven to 350°F (175°C). Grease and line two 9-inch round cake pans.

4. In a large bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and salt.

5. In a separate bowl, blend sugar, vegetable oil, eggs, buttermilk, white vinegar, vanilla extract, and red gel food coloring until smooth.

6. Gradually combine the wet ingredients with the dry ingredients, mixing just until smooth to avoid overmixing.

7. Divide the batter evenly between the two pans and bake for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean. Let the cake layers cool completely.

8. In a medium bowl, beat softened cream cheese and sugar until smooth and creamy. Add eggs one at a time, beating well after each addition. Mix in vanilla extract and sour cream or heavy cream until fully incorporated.

9. Pour the cheesecake batter over the cooled cookie crust (or into a prepared pan if not using the crust). Bake at 325°F (160°C) for 40 to 45 minutes, just until the cheesecake is set but still slightly jiggly in the center. Allow to cool fully and then chill in the refrigerator.

10. Assemble the cake by placing one red velvet cake layer on your serving plate and spreading a thin layer of cream cheese frosting on top. Add the chilled cheesecake layer, spreading a light layer of frosting on it, then top with the second red velvet cake layer.

11. Cover the entire cake with remaining cream cheese frosting. Warm the strawberry or raspberry jam with water and lemon juice until pourable, then gently pour it over the top of the cake. Decorate with piped cream cheese frosting, red velvet cake crumbs, and dark chocolate chips.