Preheat the oven to 375 °F. Lightly spray a 9x13-inch baking dish with nonstick spray.
In a large bowl, mash 3 bananas with a potato masher.
Whisk in the maple syrup
Beat in 1 egg and ¼ cup egg white
Whisk in the rum extract, vanilla extract, baking powder, salt, cinnamon and nutmeg
Stir in the milk
Stir in the oats
Stir in the chopped pecans
Pour the mixture into the prepared baking dish. Bake at 375 °F for 45 minutes. It's done when the oatmeal is golden-brown. A toothpick/knife/skewer inserted into the center of the oatmeal should come out clean.