Preheat the oven to 400 degrees F (200 degrees C). Grease cookie sheets.
Sift flour, baking powder, salt, and baking soda together in a large bowl.
Beat sugar and butter together in a separate large bowl with an electric mixer until light and fluffy. Add bananas, eggs, and vanilla; beat to combine. Gradually blend in flour mixture until just combined; stir in chocolate chips. Drop dough by teaspoonfuls onto prepared cookie sheets.
Bake in the preheated oven for 12 to 15 minutes. Transfer cookies to a wire rack to cool completely.