Preheat oven to 350°F (175°C)
In a large mixing bowl, cream together softened butter and granulated sugar until light and fluffy.
Beat in eggs, one at a time, until fully incorporated.
Mash ripe bananas in a separate bowl and stir in banana extract and vanilla extract.
Add mashed bananas and extracts to the butter-sugar mixture and mix well to combine.
In a separate bowl, sift together flour and pudding mix.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined; avoid overmixing.
Cover the dough and refrigerate for 30 minutes to firm up and enhance flavor.
After chilling, scoop dough into 1 1/2-inch balls and place on parchment-lined baking sheets, spacing at least 2 inches apart.
Bake for 10-12 minutes or until golden around the edges but still soft in the center.
Cool cookies on the baking sheet for 5-10 minutes before transferring to wire racks to cool completely.
Optional: Add a simple vanilla glaze or decorations, if desired, after cooling.