Begin by creaming together the softened butter, granulated sugar, and brown sugar in a large mixing bowl until the mixture becomes light and fluffy. Next, incorporate the instant banana cream pudding mix, room temperature eggs, and vanilla extract. In a separate bowl, whisk together the all-purpose flour, baking soda, and salt, then gradually blend this dry mixture into the creamed ingredients. Finally, fold in the white baking chips. Cover the dough and refrigerate for 30 minutes.

Preheat your oven to 350°F. Shape the chilled dough into 1-inch balls and arrange them two inches apart on parchment-lined baking sheets. Lightly sprinkle the formed dough with the crushed vanilla wafers. Bake the cookies for 8 to 10 minutes, or until the edges are just beginning to turn golden brown. Allow the cookies to cool on the pan for 10 minutes before transferring them to wire racks to cool completely.