Preheat your oven to 350°F (175°C).
In a large bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.
Mix in the mashed bananas, eggs, and vanilla extract until well combined.
In a separate bowl, whisk together the flour, baking soda, salt, and vanilla pudding mix.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Scoop tablespoon-sized portions of cookie dough onto a baking sheet lined with parchment paper.
Gently press a slice of banana onto the top of each cookie.
Bake for 12-15 minutes, or until the edges are lightly golden.
Remove from the oven and let cool on the baking sheet for 5 minutes before transferring to a wire rack.
Enjoy your delicious banana pudding cookies with a glass of milk!