Pour half-and-half and pureed strawberries into a large bowl. Add pudding mix. Beat with wire whisk until well blended, 1 to 2 minutes. Let stand 5 minutes or until slightly thickened. Line bottom of crust with banana slices. Fold cool whip into pudding mixture. Spoon into crust. Freeze until firm, about 6 hours or overnight. Remove from freezer. Let stand a t room temperature about 10 minutes before serving to soften. Garnish with whipped topping, maraschino cherries, and chipped nuts. Serve with remaining strawberries, pureed, if desired.