Whisk together the flour, baking soda, corn starch, and salt in a medium bowl and set aside.
Cream butter, bananas, and sugars together until combined.
Add vanilla extract and mix until combined.
Stir in the flour mixture just until combined.
Stir in chocolate and peanut butter chips.
Cover and refrigerate dough for 30 minutes.
Preheat oven to 375F. Line two cookie sheets with parchment paper.
Use a cookie scoop to scoop out cookie dough onto prepared cookie sheets.
Bake cookies for 10 to 12 minutes or just until they start to turn light, golden brown on top.
Let cookies cool completely on cookie sheets.
Store in airtight containers for up to a week.