Position rack in center of oven and preheat to 350 degrees F. Butter a 9-inch springform pan. Dust pan lightly with flour, tap out excess.
In a microwave-safe bowl combine chocolate and butter and heat in microwave until melted and smooth. Cool. Whisk flour, salt, and baking powder in a small bowl to blend. Using an electric mixer, beat eggs and brown sugar in a medium bowl until very thick, about 4 minutes. Scrap down the sides of the bowl. Beat in melted chocolate mixture and vanilla. Add flour mixture and beat until just blended.
Spread 1 cup brownie batter over bottom of prepared pan, reserving remaining batter. Bake until firm, 15-17 minutes. Cool bottom crust in pan in freezer for 15 minutes. Maintain oven temperature.
For the filling:
Blend cream cheese and brown sugar in the bowl of a food processor until smooth. Add eggs and sour cream and pulse until mixture is smooth, scraping down the sides of bowl as necessary. Add peanut butter and pulse until combined.
Using a small offset spatula or knife, spread remaining brownie batter evenly around sides of pan, sealing batter to bottom crust. Pour in filling (filling will not be as high as brownie batter).
Bake until center of cheesecake is set and brownie sides have fallen to form 1-inch-wide ring around filling, about 30 minutes. Set cake on rack to cool completely before covering pan with foil and chilling in the fridge overnight.