Prep the pan: Heat the oven to 350°F (175°C). Line an 8x8-inch pan with parchment paper, leaving overhang for easy lifting.
Lightly grease the sides if needed.
Mash the bananas: In a large bowl, mash 3 ripe bananas until mostly smooth with just small lumps. You should have about 1 to 1 1/4 cups mashed.
Whisk in wet ingredients: Add 1 large egg, 1/3 cup unsweetened applesauce (or yogurt), 1 teaspoon vanilla, and stir until combined.
Add the dry ingredients: Stir in 2 cups rolled oats, 1 teaspoon baking powder, 1 teaspoon cinnamon, and a small pinch of salt. If using add-ins like 1–2 tablespoons chia or hemp seeds, fold them in now.
The mixture should be thick and scoopable.
Spread and smooth: Transfer batter to the prepared pan. Use a spatula to spread it into an even layer, pressing into the corners.
Bake: Bake for 22–28 minutes, until the center is set and the edges are lightly golden. A toothpick should come out with a few moist crumbs, not wet batter.
Cool completely: Let the pan cool on a rack for at least 30 minutes.
Lift out using the parchment and cut into small bars or squares sized for your child’s grip.
Serve: Offer plain, or with a thin swipe of nut or seed butter for extra protein and healthy fats if appropriate for your child’s age.