Preheat the oven to 325°F. Spray an 8.5-inch springform pan with cooking spray and line the bottom with parchment paper. Wrap the pan in two layers of aluminum foil to prevent water from leaking in during the water bath.

In a mixing bowl, combine softened cream cheese, sugar, and vanilla extract until just blended. Add the slightly beaten eggs and mix on low speed until incorporated—avoid overmixing. Gently fold in the sour cream, followed by the melted chocolate.

Pour the cheesecake batter into the prepared springform pan and smooth the top.

Place the springform pan into a larger roasting pan and pour hot water into the roasting pan until it reaches halfway up the sides of the springform pan. Bake for 40-50 minutes, or until the edges are set, and the center is slightly jiggly but firm to the touch.

Remove the springform pan from the water bath and let it cool at room temperature. Refrigerate for at least 4 hours or overnight.

Preheat the oven to 350°F. Grease two 8.5-inch round cake pans, line the bottoms with parchment paper, grease the paper, and dust the pans with flour.

In a large bowl, whisk together the dry ingredients: sugar, flour, cocoa powder, baking powder, baking soda, and salt.

Add the eggs, milk, vanilla extract, and vegetable oil to the dry mixture. Beat on medium speed for 2 minutes. Slowly stir in the boiling water until just combined (the batter will be thin).

Divide the batter evenly between the prepared pans. Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean with a few moist crumbs.

Cool the cakes in their pans for 10-15 minutes, then invert them onto a wire rack to cool completely.

Once the cakes are cooled and the cheesecake is firm, prepare the frosting.

In a bowl, whisk together melted butter and cocoa powder. Gradually add powdered sugar, milk, and vanilla extract, mixing until smooth. Adjust the consistency as needed: add milk, one tablespoon at a time, if the frosting is too thick, or add more powdered sugar if it’s too thin.

Place one chocolate cake layer on a serving plate and spread a thin layer of frosting on top.

Remove the cheesecake from the refrigerator. Take off the aluminum foil, release the springform pan ring, and run a thin metal spatula under the cheesecake to release it from the base. Carefully transfer the cheesecake onto the frosted cake layer (alternatively, invert the cheesecake onto the cake layer, remove the pan base, and peel off the parchment paper).

Spread a thin layer of frosting on top of the cheesecake.

Place the second chocolate cake layer over the cheesecake. Cover the top and sides of the cake with the remaining frosting, smoothing it evenly.

Garnish the sides of the cake with chocolate chips. Store the assembled cake in the refrigerator.