Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, cream together the softened butter and brown sugar until light and fluffy.
Mix in the mashed banana, eggs, and vanilla extract until smooth.
In a separate bowl, whisk together the flour, banana pudding mix, and baking soda.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Fold in the White Chocolate Chips.
Lightly oil your hands and roll the dough into small balls, placing them on the baking sheet about an inch apart.
Pop them into the oven for 10-12 minutes, or until the edges turn golden brown.
Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack. Then, dive in!