Preheat oven to 350°F (176°C). Line a 9-inch springform pan with parchment paper on the bottom and grease the sides.

In a medium bowl, combine the melted butter, 1 cup sugar, and 1 tsp vanilla extract.

Add the 2 eggs and mix until well combined.

In another medium bowl, whisk together the 0.75 cup all-purpose flour, cocoa powder, baking powder, and salt.

Add the dry ingredients to the wet mixture and mix until just combined.

Pour the brownie batter into the prepared pan and spread evenly. Bake for 20-25 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.

While the brownie bakes, in a large bowl, beat the cream cheese, 1 cup sugar, and 3 tbsp all-purpose flour on low speed until completely combined and smooth. Scrape down the sides of the bowl frequently to prevent air bubbles.

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

In a small bowl, combine the Kahlua and instant coffee granules, stirring until the granules are dissolved. Add this mixture and 2 tsp vanilla extract to the cream cheese mixture and mix on low speed until well combined.

Add the 3 large eggs one at a time, mixing slowly after each addition until just combined. Do not overmix.

Once the brownie is done, reduce the oven temperature to 300°F (148°C). Remove the brownie from the oven and pour the cheesecake batter evenly over the brownie.

Wrap the outside of the springform pan with aluminum foil. Place the springform pan inside a larger pan and fill the larger pan with enough warm water to go about halfway up the sides of the springform pan, ensuring water does not go above the foil.

Bake for 1 hour 15 minutes. The center should be set but still slightly jiggly.

Turn off the oven and leave the door closed for 30 minutes. Then, crack the oven door open for another 30 minutes to allow for slow cooling, which helps prevent cracks.

Remove the cheesecake from the oven and water bath. Refrigerate until firm, about 5-6 hours or overnight. Once completely cool and firm, carefully remove from the springform pan.

To make the ganache, place the chocolate chips in a small heatproof bowl. In a glass measuring cup, combine 5 tbsp heavy whipping cream and 5 tbsp Kahlua and heat until it just begins to boil.

Pour the hot liquid over the chocolate chips and let sit for 2-3 minutes, then whisk until smooth. Pour the chocolate ganache onto the cooled cheesecake and spread evenly.

To make the Kahlua whipped cream, add 0.5 cup heavy whipping cream, 2 tbsp Kahlua, and powdered sugar to a large mixer bowl. Whip on high speed until stiff peaks form.

Pipe the whipped cream onto the top of the cheesecake. If desired, sprinkle with a little extra cocoa powder.

Refrigerate the cheesecake until ready to serve. Best enjoyed within 3-5 days.