In a large mixing bowl, combine the softened cream cheese and vanilla pudding mix. Beat on medium speed until smooth, about 2-3 minutes. Gradually pour in the cold milk while mixing until creamy and lump-free.

Gently fold in 11 oz of Cool Whip into the creamy mixture. Reserve ½ cup of Cool Whip for topping.

Spread a thin layer of reserved Cool Whip on the bottom of a 9x13-inch pan. Place 5 graham crackers side by side in the pan.

Spread half of the creamy filling over the graham crackers. Layer half of the sliced strawberries and blueberries on top.

Add another layer of graham crackers, followed by the remaining filling and top with remaining strawberries and blueberries.

Cover the pan with plastic wrap and refrigerate for at least 4 hours or overnight.

Melt the white chocolate chips in a microwave-safe bowl and drizzle over the chilled cake before serving.