Preheat the oven to 350º Fahrenheit. Line two baking sheets with parchment paper and set aside.
Cream butter and sugar with an electric mixer for several minutes until the mixture creates air bubbles. Beat in both eggs until the batter is light and fluffy.
Add the mashed bananas. Continue to be until well combined.
Add dry ingredients (banana cream pudding mix, flour, baking soda, and salt) and continue to beat until the batter is smooth. Fold in white chocolate chips.
Use a cookie scoop to drop the cookies dough on the baking sheet. About a tablespoon per cookie.