In a medium bowl, whisk together the flour, baking soda, and salt, then set it aside.
In a separate large bowl, beat the melted butter, white sugar, and brown sugar together for about two minutes until the mixture looks light and creamy.
Mash the ripe bananas until smooth, then add them into the butter mixture along with the vanilla extract and egg yolk. Mix on medium speed until everything is fully combined and the batter smells sweet and banana-rich.
Slowly add the dry ingredients into the wet mixture, mixing on low speed just until the flour disappears.
Be careful not to overmix. Gently stir in the Nilla wafer crumbs and white chocolate chips, a few bigger pieces in the crumbs are totally fine for extra texture.
Rest the dough at room temperature for 15 minutes to help it firm. During this time, set your oven to 350°F and line two baking sheets with parchment paper.
Scoop the cookie dough using a 2-tablespoon cookie scoop and place six dough balls on each baking sheet, making sure to leave space between them.
Bake one sheet at a time for 10–12 minutes, just until the edges are lightly golden and the centers still look soft.
Cool the cookies on the baking sheet for five minutes, then carefully transfer them to a wire rack to cool down fully.
While the cookies cool, prepare the whipped cream vanilla pudding topping. Combine the pudding mix, milk, and vanilla extract in a bowl, beating until the mixture reaches a thick texture.
Chill a metal bowl and whisk, then whip the heavy cream until stiff peaks form. Gently fold the whipped cream into the pudding mixture, being careful not to deflate it.
Once the cookies are completely cool, spoon a generous dollop of the whipped pudding mixture onto each one.
Spread it out gently and top each frosted cookie with a Nilla wafer for the perfect finishing touch.