Preheat your oven to 350°F (175°C).
Cream together the softened unsalted butter, brown sugar, and white sugar until light and fluffy, about 2-3 minutes.
Add the 2 large eggs and 1 egg yolk, along with the vanilla extract. Beat until well combined.
Mix in the banana instant pudding mix until fully combined.
In a separate bowl, whisk together the flour, baking soda, and salt, then gradually add to the wet ingredients.
Fold in the white chocolate chips until evenly distributed.
Using a cookie scoop, drop balls of dough onto a baking sheet lined with parchment paper, leaving space between each.
Bake for 10-12 minutes, or until the edges are golden brown. Let cool on the baking sheet for a few minutes before transferring to a cooling rack.