Preheat the oven to 225°. Grease the sides of a 9 inch springform pan (sides should be 3 inches high). Line the bottom of the pan with parchment paper.
In a large mixing bowl, beat the cream cheese and sugar on high speed for 3 minutes or until smooth and creamy. Add the eggs and egg yolks 1 at a time, scraping down the sides of the bowl occasionally. Add the vanilla and salt then beat for 30 seconds to blend well. Beat in the sour cream on low speed until well combined, be sure to stop the mixer to scrape down the sides of the bowl.
Pour half of the batter into the prepared pan. Drop 5 to 6 tablespoons each of hot fudge sauce and caramel sauce on top of the batter then use a knife to swirl the sauces into the batter. Pour the remaining batter on top and repeat with the caramel and chocolate sauce swirl. The springform pan will be very full.
Place the springform pan in the center of the oven. Bake for 75 minutes. The cheesecake will appear jiggly in the center, this is normal, it will firm up after it is completely cooled (if your concerned that it hasn't cooked long enough, check the center of the cheesecake with an instant read thermometer. It should read 150°F). Turn off the oven and let the cake sit in the oven for 1 hour, keep the door closed while it slowly cools down. Remove from oven and cool on a rack for 1 hour until it reaches room temperature. When cooled, cover with plastic wrap and place in the refrigerator for 8 to 12 hours. (The cheesecake will be jiggly in the center when you remove it from the oven but will firm up after it is refrigerated.)
Bake Brownie Bottom
Preheat oven to 350°F. Grease a 9-inch round baking pan and line the bottom with parchment paper.
Melt the butter and chocolate in a microwaveable bowl. Set aside to let cool.
Whisk the flour, baking powder, and salt together in a small bowl.
Beat the sugar, eggs, vanilla and coffee granules in a large bowl, then add the chocolate mixture, stir to combine. Stir in flour mixture then pour the batter into the prepared baking pan.
Bake 25 to 30 minutes until shiny and crackly on top. Remove from the oven and cool on a wire rack.
Whipped Cream Topping
Chill a mixing bowl and the beaters (or a whisk) in the freezer for a few minutes.
Place the cream, sugar and vanilla in the cold bowl and begin beating on medium high speed until the beaters or whisk leave tracks in the cream. At this point slow the mixer down to medium speed and check it frequently. You want to stop when the cream has billowy mountains when you lift the beater or whisk out of it.
Unmold Cheesecake and Assemble
Run a knife or metal spatula around the sides of the cheesecake and open the latch of the springform pan to release it from the cheesecake. Place a plastic-wrapped plate or cake board on top of the cheesecake and invert. Remove the bottom of the pan and the parchment then place the brownie layer on the bottom of the cheesecake. Re-invert onto a serving plate so the brownie is flipped to the bottom.
Drizzle additional chocolate and caramel sauce over the top of the cheesecake. Garnish with whipped cream and pecans if desired.
Notes
This cheesecake does not need a water bath because it is baked at a very low temperature.
If you are not certain that the cheesecake is completely cooked, remove it from the oven, close the oven door to keep the heat in and check the center of the cheesecake with a thermometer. If it reads 150°F in the center, it is done. Place it back in the hot oven. If it has not reached 150°F then let it continue cooking but if it has reached 150°F then turn the oven off and let it cool off slowly as the oven cools down.