Mix flour, baking soda, corn starch and salt. Set aside.
Cream butter, bananas and sugars until light and fluffy. Then stir in vanilla.
Stir in dry ingredients until mixed. Add chocolate and white chocolate chips.
Refrigerate dough for 30 minutes to 1 hour.
Preheat oven to 375 degrees Fahrenheit. Line a cookie sheet with parchment paper (or nonstick spray or oil will also work).
Scoop out dough by tablespoons (if the dough is cold enough you can roll the dough into balls), and put on cookie sheet.
Bake 7-9 minutes (7 minutes are perfect for us to keep them soft and chewy).
Let cool for 10 minutes. Serve.