Step 1

Place 2 sticks unsalted butter in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Place 1 large egg yolk in a small bowl. Let the butter and egg yolk sit at room temperature until the butter is softened, 1 to 1 1/2 hours.

Step 2

Meanwhile, place 2 cups all-purpose flour, 1 (3.4-ounce) box instant vanilla pudding mix, 1 1/4 teaspoons kosher salt, 1/2 teaspoon baking soda, and 1/4 teaspoon baking powder in a medium bowl and whisk to combine. Place 24 Nilla wafers in a large zip-top plastic bag, seal, and crush lightly with a rolling pin or bottom of a heavy pan into 1/4 to 1/2-inch pieces (about 1 cup).

Step 3

Arrange 2 racks to divide the oven into thirds and heat the oven to 350ºF. Line 2 rimmed baking sheets with parchment paper.

Step 4

Add 2/3 cup packed light brown sugar and 1/3 cup granulated sugar to the bowl with the butter. Beat with the paddle attachment the butter and sugars on medium speed until well combined, lightened in color, and creamy, 30 seconds to 1 minute, stopping and scraping the sides of the bowl down with a flexible spatula as needed.

Step 5

Peel 1 large ripe banana, break into a few pieces, and place in a small bowl. Mash witih a fork until completely broken down with no big chunks remaining (about 1/2 cup).

Step 6

Add the banana, egg yolk, and 1 1/2 teaspoons vanilla extract to the butter mixture and beat on medium speed until incorporated and lightened in color, 20 to 30 seconds, scraping down the sides of the bowl as needed. This mixture will look slightly broken and curdled.

Step 7

Add the flour mixture to the butter mixture and beat on the lowest speed until just combined, about 20 seconds. Some dry bits remaining are okay.

Step 8

Add the Nilla wafers and 3/4 cup white chocolate chips. Fold together by hand with a flexible spatula until the wafers and chocolate chips are well distributed and no floury bits remain.

Step 9

Scoop out 6 (about 2 rounded tablespoon) portions of the dough onto each baking sheet, spacing them evenly apart. Refrigerate the remaining dough.

Step 10

Bake for 7 minutes. Rotate the baking sheets from front to back and top to bottom. Bake until the cookies are set and light golden brown around the edges, 4 to 6 minutes more. Let the cookies cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely. Repeat baking the remaining cookie dough on cooled baking sheets (you can reuse the parchment).