Heat oven to 350. Grease 8 or 9-inch square baking pan. Stir together butter, sugar and vanilla in bowl. Add eggs; beat well with spoon. Stir together flour, cocoa, baking powder and salt; gradually add to egg mixture, beating until well blended. Spread batter in prepared pan. Bake 20 to 25 minutes or until brownies begin to pull away from sides of pan. Cool completley in pan on wire rack.
Combine all crust ingredients and press onto bottom and up sides of a 9-inch springform pan. Bake 8 minutes at 350.
Beat cream cheese, sugar and vanilla until smooth. Gradually add eggs, beating well after each addition. Pour batter into prepared crust.
Cut cooled brownies into 3/4-inch pieces and sprinkle over cheesecake batter, gently pushing them down into the batter. Drop peanut butter topping by teaspoonfuls onto surface of cheesecake. With knife or metal spatula, swirl gently through batter for marbled effect. Bake 50 to 55 minutes or until almost set. Remove from oven to wire rack. With knife, loosen cake from side of pan; cool.
Cover and place in refrigerator until chilled through, about 4 hours.