1. Preheat oven to 350°F (176°C). Line a 9-inch (23cm) springform pan with parchment paper in the bottom and grease the sides.
2. In a medium sized bowl, combine the flour, cocoa, baking powder and salt. Set aside.
3. In a large bowl, combine the butter, sugar and vanilla extract.
4. Add the eggs and mix until well combined.
5. Add the dry ingredients to the egg mixture and mix until well combined.
6. Pour the batter into the prepared pan and spread evenly.
7. Bake for 20-25 minutes, or until a toothpick comes out with a few moist crumbs.
8. When the brownie is done baking, reduce the oven temperature to 300°F (148°C). Remove the brownie from the oven and allow to cool for about 10 minutes.
9. Remove the sides of the springform pan, wash, respray with non-stick spray and reattach to the springform pan bottom, with the brownie still on it. You can skip this step, but I find that the edges of the final cheesecake look best if you wash the sides of the pan before adding the cheesecake filling.

TO MAKE THE CHEESECAKE FILLING:

1. In a large bowl, beat the cream cheese, sugar and flour on low speed until well completely combined and smooth. Be sure to use low speed to reduce the amount of air added to the batter, which can cause cracks. Scrape down the sides of the bowl.
2. In a small bowl, combine the hot water and coffee granules and stir until the granules are dissolved.
3. Add the sour cream, espresso mixture and extracts to the cream cheese mixture and mix on low speed until well combined.
4. Add the eggs one at a time, mixing slowly to combine after each addition. Scrape down the sides of the bowl as needed to make sure everything is well combined.
5. Pour the cheesecake batter evenly over the brownie.
6. Wrap the outside of the pan with aluminum foil, then place the springform pan inside another larger pan. Fill the outside pan with enough warm water to go about halfway up the sides of the springform pan. The water should not go above the top edge of the aluminum foil on the springform pan.
7. Bake for 1 hour 15 minutes. The center should be set, but still jiggly.
8. Turn off the oven and leave the door closed for 30 minutes. The cheesecake will continue to cook, but slowly begin to cool as well.
9. Crack the door of the oven for 30 minutes to allow the cheesecake to continue to cool slowly. This process helps prevent cracking.
10. Remove the cheesecake from the oven and water bath wrapping and refrigerate until firm, 5-6 hours or overnight. Once completely cool and firm, remove from the springform pan and place on a serving plate.

TO FINISH OFF THE CHEESECAKE:

1. To make the ganache, add the white chocolate chips and peppermint extract to a small to medium sized bowl.
2. Heat the heavy whipping cream until it begins to boil, then pour over the white chocolate chips. Allow to sit for 2-3 minutes, then whisk until smooth. If it doesn’t smooth out completely, microwave the mixture for another 10-20 seconds, then whisk until smooth.
3. Add the peppermint chips and stir to incorporate.
4. Spread the ganache evenly over the top of the cheesecake.
5. To make the whipped cream, add the cream, powdered sugar and peppermint extract to a large mixer bowl and whip on high speed until stiff peaks form.
6. Color the whipped cream with red gel icing color, then pipe around the edges of the cheesecake.
7. Sprinkle a few peppermint pieces around the top of the cheesecake.
8. Refrigerate cheesecake until ready to serve. Cheesecake is best when well covered and refrigerated and lasts well for 3-4 days.