Preheat oven to 350°F. Grease a 9-inch springform, line bottom with parchment, wrap pan in foil. Whisk melted butter and the first 1 cup sugar. Whisk in the 2 eggs and 1 tsp vanilla. Stir in cocoa, flour, salt, and baking powder until just combined. Spread into pan.

Par-bake for 18–20 minutes until edges set and center is slightly soft. Remove from oven, lower heat to 325°F.

Beat cream cheese and second 1 cup sugar on low until smooth. Mix in sour cream and 1 tbsp vanilla. Add 3 eggs one at a time, mixing just until incorporated.

Pour cheesecake over warm brownie. Tap pan on counter. Set in a roasting pan, pour hot water halfway up the sides. Bake at 325°F for 55–65 minutes, until edges are set and center jiggles slightly. Turn off oven, prop door open, cool inside for 1 hour.

Remove from water bath, cool to room temperature, then refrigerate at least 4 hours. Run knife around edge, release ring, slice with a hot dry knife.