Preheat your oven to 350°F and line a baking sheet with parchment paper. In a large mixing bowl, mash your ripe bananas thoroughly with a fork until they're mostly smooth — a few small lumps are totally fine and will add a little texture to the finished cookies.
Add the peanut butter, honey, and vanilla extract to the mashed bananas and stir everything together until well combined. The mixture will be thick and slightly sticky, which is exactly what you want here.
Pour in the rolled oats, cinnamon, nutmeg, salt, and ground flaxseed. Stir everything together until no dry spots remain and the oats are fully coated in that banana mixture. Fold in the chocolate chips last so they stay evenly distributed throughout the dough.
Using a large spoon or a cookie scoop, drop portions of the dough onto your prepared baking sheet, spacing them about an inch apart. Gently press each one down with the back of your spoon into a round cookie shape, since these won't spread much on their own during baking.
Bake for 13 to 15 minutes, until the edges look set and the tops are lightly golden. Let them cool on the baking sheet for at least 5 minutes before moving them — they firm up as they cool and are much easier to handle once they've had a chance to rest.