Beat pudding mix and milk in medium bowl with whisk 2 min. Refrigerate 5 min. Stir in 1 cup Cool Whip
and chopped berries. Unroll cake; remove towel. Spread strawberry mixture over cake, leaving 1-inch border around all sides. Reroll cake; wrap in plastic wrap. Refrigerate 1 hour. Unwrap just before serving; place, seam-side down, on platter. Frost with remaining Cool Whip
. Top with remaining berries.