Prepare a 9-inch cake pan or springform pan with parchment paper in the bottom and grease the sides. Preheat the oven to 350°F.

Combine the flour, baking powder and salt in a medium-sized bowl and set aside.

Add the butter, sugar, oil and vanilla extract to a large mixer bowl and beat together until light in color and fluffy, about 3-4 minutes.

Add the egg to the creamed butter and sugar mixture, mixing until mostly combined. Scrape down the sides of the bowl as needed.

Add half of the dry ingredients to the batter and mix until mostly combined.

Slowly add the milk and mix until well combined. The batter will look a little curdled, but that’s ok.

Add the remaining dry ingredients and mix until well combined and smooth. Do not overmix the batter.

Spread the cake batter evenly into the bottom of the prepared pan and bake for 13-15 minutes, or until a toothpick comes out with a few crumbs.

Remove the cake from the oven and allow it to cool for about 2-3 minutes, then transfer it to a cooling rack to cool completely. Set aside.

While the cake is cooling, add the espresso coffee powder and sugar to the hot water and stir to dissolve, then add the Kahlua. Set aside.

Add the cream cheese, mascarpone cheese, sugar and flour to a large mixer bowl and beat on low speed until combined and smooth. Scrape down the sides of the bowl.

Add the sour cream and vanilla extract and mix on low speed until well combined.

Add the eggs and egg yolks one at a time, mixing slowly to combine after each addition. Scrape down the sides of the bowl as needed.

Reduce the oven temperature to 300°F. Prepare a springform pan with parchment paper in the bottom and grease the sides.

Reset the springform pan edges around the cake layer and drizzle 6-7 tablespoons of the espresso mixture evenly over the cake.

Set aside about 2 cups of the cheesecake filling, then add the remainder of the cheesecake filling to the pan and spread evenly.

One at a time, dip each ladyfinger in the remaining espresso mixture, then add it to the pan on top of the cheesecake filling. Make an even layer, breaking the ladyfingers if needed.

Pour the reserved cheesecake filling over the top of the ladyfingers, using a spoon to drop spoonfuls, then spreading them evenly.

Prepare the pan for a water bath by wrapping the outside of the pan with aluminum foil, then place the springform pan inside another larger pan. Fill the outside pan with warm water about halfway up the sides of the springform pan.

Bake the cheesecake for about 1 hour and 15 minutes. The center should be set, but still jiggly.

Turn off the oven and leave the door closed for 30 minutes.

Crack open the door of the oven for 30 minutes to allow the cheesecake to continue cooling slowly.

Remove the cheesecake from the oven and the water bath, then refrigerate it until firm (at least 5-6 hours, or overnight). Once cool and firm, remove it from the springform pan.

Combine the egg yolks and sugar in a double boiler or metal bowl over simmering water. Whisk to combine until the mixture thickens and turns pale yellow (about 160°F).

Set the egg mixture aside to cool to a little warmer than room temperature.

Whip the heavy whipping cream in a large mixer bowl until stiff peaks form.

When the egg mixture has cooled, add the mascarpone cheese and gently fold together until combined.

Gently fold the whipped cream into the mascarpone/egg mixture in two parts.

Remove the cheesecake from the springform pan and set it on a serving platter. Spread the topping evenly onto the cheesecake, then sprinkle with cocoa powder.

Enjoy or refrigerate until ready to serve.