Preheat oven to 375°F (190°C) and lightly grease an 8x8 inch baking dish with non-stick spray or butter.
In a large mixing bowl, whisk together the rolled oats, baking powder, salt, and ground cinnamon.
In a separate medium bowl, combine the mashed bananas, peanut butter, milk, egg, maple syrup, and vanilla extract, whisking until the peanut butter is fully integrated.
Pour the liquid mixture over the dry oats and stir until thoroughly combined.
Transfer the oatmeal mixture into the prepared baking dish, smoothing the surface with a spatula.
Bake for 30 to 35 minutes, or until the edges are golden and the center is firm to the touch.
Allow the baked oatmeal to cool in the pan for at least 10 minutes before slicing into squares and serving.