Preheat the oven to 180°C (350°F) and line a baking sheet with parchment paper.
If you have a food processor, blend the bananas, dates, peanut butter, and coconut oil until completely smooth. Otherwise, add to a large bowl and mash very well with a fork.
Drop about two tablespoons for each cookie onto the prepared baking sheet. They should be spaced about 3cm (1 in.) from each other but won't spread much.
Bake for 16-18 minutes, until the tops are lightly golden.
Remove from the oven and place the baking sheet on a cooling rack for a couple of minutes, or until the cookies can be handled. Remove and cool completely on the rack.
Refrigerate in a sealed container for up to a week or freeze up to a month.
Video
Notes
To make these nut-free, sub sunflower seed butter for the peanut and use seeds instead of nuts in the dough.