Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or lightly grease it.
In a large bowl, mash the ripe bananas until smooth. Add the applesauce, oil (or melted butter), peanut butter, and vanilla extract. Stir until everything is well combined.
Add in the rolled oats, whole wheat flour, baking powder, baking soda, and a pinch of salt. Mix until just combined. If the dough feels too wet, add an additional tablespoon or two of flour to help it firm up.
Using a spoon or cookie scoop, drop spoonfuls of dough onto the prepared baking sheet. Space them about 2 inches apart. Gently flatten the dough with the back of the spoon or fork to your desired thickness.
Bake for 12-15 minutes, or until the cookies are golden around the edges and firm in the center.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.