Heat oven to 350°F. Grease bottom of 10-inch springform pan with removable bottom.
Combine brownie mix, water, oil and 3 eggs in large bowl. Stir in walnuts. Pour into prepared pan.
Bake in 350°F oven 25 to 30 minutes. Cool on rack 15 minutes.
Combine raspberries and 1/2 cup of the raspberry jam in small bowl.
Beat cream cheese in large bowl at medium speed until smooth. Add granulated sugar, vanilla and the remaining 3 eggs, and beat until well blended.
Spoon raspberry mixture evenly over top of brownie in pan. Slowly pour cheesecake batter on top.
Bake in 350°F oven 55 minutes or until cheesecake in center is slightly set. Remove to wire rack to cool. Refrigerate cooled cake overnight.
To serve, prepare raspberry drizzle. Heat the remaining 1/4 cup raspberry jam in small saucepan over low heat until just melted. Let cool 10 minutes. Spoon confectioners sugar into small sieve; sprinkle over cake. Drizzle top of cake in zigzag pattern with raspberry jam. Refrigerate until ready to serve. Garnish with raspberries if you wish.