Prepare the pan and banana. Heat a conventional oven to 350°F (175°C). Lightly grease an 8-inch square pan at least 2 inches deep. Mash the peeled bananas thoroughly and weigh 300 g of mash. Stir the peanut butter in its jar before weighing it so the measured portion contains both its solids and dispersed oil.

Whisk the banana mixture. Whisk mashed banana and peanut butter in the larger bowl until combined. Whisk in the eggs, then gradually add the milk, maple syrup, and vanilla. If the peanut butter is stiff, loosen it first with a few spoonfuls of the measured milk. Scrape the bowl so no thick peanut butter remains stuck underneath.

Combine the dry ingredients. Stir rolled oats, baking powder, cinnamon, and salt in a separate bowl. Mix well enough that cinnamon does not sit in one concentrated pocket. There is no need to grind the oats or add flour; the eggs and hydrated oats provide the structure for this particular breakfast bake.

Fill the baking pan. Stir the dry oat mixture into the banana mixture until all the oats are moistened. Pour into the prepared pan and level the surface, checking that liquid and oats are spread evenly into the corners. Bake promptly instead of leaving the mixed pan at room temperature while doing other preparation.

Bake the center through. Bake about 38–45 minutes. The edges should be lightly browned and the middle set without loose liquid when gently moved. Check the center with a food thermometer for at least 160°F (71°C). A thick banana mixture can look set on top while remaining too soft underneath, so check the middle rather than the edges alone.

Rest and divide. Let stand for 10 minutes before dividing into nine squares or spooning into bowls. Warm portions are soft. If saving some for later, place them in shallow containers and refrigerate promptly, then cover for storage. Do not wait for the whole pan to become cold on the counter before putting leftovers away.