Preheat your oven to 350°F (175°C). Cream together the softened unsalted butter, granulated sugar, and packed brown sugar until light and fluffy, about 2-3 minutes. Beat in the eggs one at a time, followed by vanilla extract and mashed bananas. In a separate bowl, whisk together flour, baking soda, and salt. Gradually fold dry ingredients into the wet mixture and incorporate white chocolate chips.

Line a baking sheet with parchment paper. Drop rounded tablespoons of the dough onto the baking sheet, spacing 2 inches apart. Bake for 12-14 minutes, until edges are golden and centers are slightly soft. Cool on baking sheet for a few minutes before transferring to a wire rack.

Whip heavy cream using an electric mixer on medium speed until soft peaks form, about 2-3 minutes. Gradually add powdered sugar and banana pudding mix, then increase speed to high and whip until fluffy.

Once cookies have cooled, dollop whipped banana cream on top. Garnish with fresh banana slices if desired. Enjoy warm.