Start by preheating your oven to 350°F. Line two large baking sheets with parchment paper or silicone mats so the cookies don’t stick to the metal.
Peel your ripe banana and place it in a small bowl. Use a fork to mash it until it is completely smooth with no large chunks remaining.
In a large mixing bowl, beat the softened butter with the granulated and brown sugars. Use an electric mixer on medium speed for about two to three minutes until the mixture looks pale and fluffy.
Add the egg and vanilla extract to the butter mixture and beat until well combined. Next, stir in your mashed banana.
In a separate medium bowl, stir together the flour, dry pudding mix, baking soda, and salt.
Turn your mixer to a low speed and slowly add the dry flour mixture to the wet ingredients. Mix just until the white streaks of flour disappear. Grab a sturdy spoon and fold in the crushed vanilla wafers and white chocolate chips
Because of the fresh fruit, this dough can be a little soft. Place the bowl in the refrigerator for at least thirty minutes before baking.
Use a tablespoon or a cookie scoop to form balls of dough about the size of a golf ball. Place them on your prepared baking sheets, leaving at least two inches of space between each one.
Slide the trays into the oven and bake for 10 to 12 minutes. You are looking for the edges to be set and a very light golden brown, while the centers should still look slightly soft.
While the cookies cool completely, make your frosting. In a cold bowl, beat the heavy cream, powdered sugar, and vanilla until stiff peaks form. This light, airy topping replaces the whipped cream usually found on top of a banana pudding trifle.
Only frost the cookies once they are totally cold to the touch, or the cream will melt and run off the sides.