In a heavy saucepan over low heat, melt chocolate chips and peanut butter, stirring frequently. Pour half into a greased 15x10x1-in. pan; chill. Set remaining chocolate mixture aside.
In another saucepan, bring butter, milk and pudding mix to a boil; boil for 1 minute, stirring constantly. Remove from the heat; pour into a large bowl; add vanilla. Gradually stir in sugar. Spread over chocolate layer in pan; chill.
Add peanuts to reserved chocolate mixture; spread over filling. Chill. Cut into 1x1-1/2-in. pieces.