Gather the ingredients for the banana pudding cookies. Preheat the oven to 350°F and line a baking sheet with parchment paper.
In a large bowl, cream the butter and sugars together. Add the eggs, instant pudding mix, and vanilla extract. Beat until smooth and well blended.
In another bowl, whisk the dry ingredients together. Add the flour mixture to the pudding mixture and stir until just combined.
Fold the vanilla wafer cookies and white chocolate chips into the banana pudding cookie dough.
Roll the cookie dough into balls, about 1 tablespoon each. Place them on the prepared baking sheet, spacing them at least 1 inch apart.
Bake for 9 to 10 minutes, or until the banana pudding cookies are set. Remove from the oven.
Let the cookies cool on the baking sheet for about 2 to 5 minutes, then transfer them to a cooling rack to cool completely.