Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium bowl, whisk together flour, baking soda, baking powder, salt, and instant vanilla pudding mix.
In a large mixing bowl, cream together softened butter, granulated sugar, and brown sugar using an electric mixer until light and fluffy.
Beat in the egg, mashed bananas, and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in chocolate chips if desired.
Drop rounded balls of dough onto the prepared baking sheet, spaced about 2 inches apart.
Bake for 10 to 12 minutes or until edges are golden and centers are set but soft.
Allow cookies to cool on the baking sheet for a few minutes, then transfer to a wire rack to cool completely.
Lightly dust cooled cookies with powdered sugar.
Serve topped with whipped cream and a slice of banana for garnish.