Cream the butter, bananas and sugars together with a mixer. Beat in the vanilla until the mixture is smooth, and then beat in the flour, baking soda, corn starch and salt. Once everything is combined, fold in the chocolate and the peanut butter chips.
Cover the bowl and leave in the refrigerator for at least 30 minutes.
Preheat the oven and prepare cookie sheets by lining them with parchment paper.
Using a one-inch scoop (or just eyeball that amount with a regular spoon), place dough onto the cookie sheets, about two inches apart.
Bake for 10 to 12 minutes or until the cookies are golden on top. Let them cool completely before transferring them from the parchment paper to an airtight container.