Preheat the oven to 350°F (180°C). Line a sheet pan with parchment paper or a silicone baking mat.
In a large bowl, mash the bananas with a sturdy whisk or a fork. Once the bananas are well mashed, add the peanut butter, maple syrup, egg, and vanilla. Whisk it together until all the ingredients are well combined.
Add the cinnamon, salt, and baking powder to the bowl then whisk it again to combine. Add the flour and oats then use a rubber spatula or large spoon to stir until the flour is just mixed in.
Use a large cookie scoop or a ¼ cup measuring cup to make 10 mounds of the sticky dough on the baking sheet. Spoon about ½ teaspoon of the jam onto the center of each cookie and press the top down slightly with the back of a spoon.
Use oven mitts to transfer the baking sheet to the oven. Set a timer for 14 minutes then check if the edges of the cookies are light golden brown. If they still look pale, set a timer for 2 more minutes.
Use oven mitts to carefully remove the pan from the oven (or ask an adult for help). Allow the cookies to cool fully before eating or storing in an airtight container for later.