Mile High Banana Cream Pie

9- inch deep dish pie shell (baked)

For the filling:

box [2.5 oz] dry whipped topping mix [i.e.Dream Whip]

half & half (divided)

box [3.4 oz] banana cream instant pudding mix

box [3.4 oz] vanilla instant pudding mix

pure vanilla extract

whipped cream cheese

large bananas (sliced)

Topping:

[8 oz] frozen whipped topping (thawed)