Preheat oven to 350 degrees F and line two baking sheets with parchment.
Cream the butter, sugars, and enrich the base
Use a stand mixer on medium speed to beat the butter and sugars until pale and fluffy, about 3 minutes.
Add the egg and vanilla and mix an additional 2-3 minutes, until glossy and cohesive.
Add the mashed banana and mix until incorporated, scraping once if you see streaks.
Fold in dries, then portion
In a small bowl, mix the dry ingredients except the vanilla cookies and white chocolate chips. Turn the mixer to low and gradually add the dry ingredients, then add the wafers and chips.
Drop cookie rounds of about 1.5 tablespoon onto cookie sheets (6 cookie dough balls per sheet), spacing them apart for spreading.
Bake and set the structure
Bake 9-11 minutes.
Cool on cookie sheets for 2 minutes before removing to wire racks.
Notes
Chill the dough for 30 minutes to 2 hours to limit spread and round out flavor. Press extra wafer crumbs into each dough ball right before baking for a more bakery-style top.Nutrition information is estimated based on common ingredients and serving sizes and may vary.