In a large mixing bowl, combine the instant vanilla pudding mix and cold milk. Using a hand mixer at medium-low speed, beat the mixture until well blended (about 2 minutes).
Chill the pudding mixture in the refrigerator while you prepare the next step.
In an 11x7-inch baking dish, arrange a single layer of vanilla wafer cookies with the flat side down. Use 24 cookies for this layer.
Pour half of the chilled pudding mixture (about 1 cup) over the cookies in the baking dish.
Add half of the thinly sliced bananas in a single layer over the pudding.
Repeat with another layer of cookies, pudding, and bananas.
Top the final layer with whipped cream, spreading it evenly over the pudding.
If desired, garnish with extra sliced bananas and cookies.
Chill the dessert in the refrigerator for at least 4 hours, up to overnight before serving.
Notes
Cookies, bananas then pudding, repeat. The pudding on top of the bananas keeps the bananas from turning dark.