1. Preheat oven to 350F. Spray an 8 or 9-inch springform pan with cooking spray.
2. Melt the butter over medium-low heat. Once butter is melted, reduce heat to low and stir in chocolate until melted. Remove from heat and stir in sugar. Add eggs, one at a time, beating after each addition. Add vanilla. Stir in flour, cinnamon, cayenne, and salt, stirring vigorously until batter is smooth.
3. Pour batter into prepared pan and bake for 30 minutes, until the center is barely set. Remove from oven and allow to cool.
4. Reduce oven temperature to 325F.
5. While brownie bottom is cooling, prepare filling. Mix cream cheese, sugar, cinnamon, and vanilla in a mixing bowl until well blended. Stir in sour cream. Add eggs, mixing on low speed, just until blended. Pour batter over cheesecake crust.
6. Place springform pan on a rimmed cookie sheet. Add 3/4-inch of water into the baking sheet. Bake at 325F for 1 hour and 5 minutes, or until center is just set (middle will jiggle slightly). Turn off the oven and crack the oven door. Allow to cool until it can be touched without hot pads. Remove from oven and cool on counter to room temperature.
7. Cover and refrigerate at least 4 hours, or overnight. To serve, run a knife around the rim of the pan to loosen cake before removing outer sides of pan. Slice into pieces and serve.