Preheat oven to 350°F. Line two baking sheets with parchment paper.
Beat the butter, brown sugar, and granulated sugar in a large bowl of a stand mixer fitted with a paddle attachment or electric mixer until creamy and light, about 2-3 minutes.
1 cup salted butter, 3/4 cup (150g) brown sugar, 1/4 cup (50g) granulated sugar
Add the eggs and vanilla extract. Beat again, scraping the bottom and sides of the bowl as needed.
2 large eggs, 2 teaspoons vanilla extract
Add the flour, pudding mix, baking soda, and salt. Mix just until combined.
2 3/4 cups (388g) all-purpose flour, 1 (3.4-ounce) box instant banana pudding mix, 1 teaspoon baking soda, 1/2 teaspoon salt
Add Nilla Wafers and white chocolate chips. Stir in with a spatula or spoon.
1 cup broken up Nilla Wafers, 1/2 cup white chocolate chips
Use a small cookie scoop to scoop mounds of cookie dough onto the baking sheets lined, spacing the cookies a couple inches apart so they have room to spread. Press a couple of pieces into the top of each mound of dough.
Bake for 8-10 minutes until set around the edges but slightly underbaked in the middle. Immediately after removing from the oven, press a few additional white chocolate chips into the tops of the cookies. Let sit for 10 minutes on the baking sheets before transferring to a wire rack to cool completely.