Mix peanut butter and butter in large bowl until well blended. Add sugars and vanilla; stir until blended and smooth. Stir in vanilla wafer crumbs and chocolate chips.
Line 8-inch square pan with foil, with ends of foil extending over sides of pan. Press 1/2 of the dough into even layer pan. Pat remaining dough on parchment or wax paper into 8-inch square. Gently spread ice cream over layer on pan. Flip 8-inch square layer onto top of ice cream. Peel back parchment paper. Cover with foil.
Freeze 3 hours or until firm. Let stand at room temperature 2 to 3 minutes to allow ice cream to soften slightly. Cut into 16 bars. Wrap each in plastic wrap. Store in freezer.