Using your fingers or a pastry brush, butter a 8-inch squared baking dish (including the sides) with softened unsalted butter and set it aside.
Shred the zucchini using the grater and measure 1/2 cup. Transfer the shredded zucchini to a kitchen towel. Gather the ends and twist the kitchen towel to help squeeze out all of its liquid. Set the zucchini aside.
Mash about 3 bananas in a bowl with a fork. Measure 1 and 1/2 cups of the mashed banana and set it aside. (Mash another banana if needed to gather 1 and 1/2 cups).
To a blender add the following ingredients: mashed banana, egg, shredded zucchini (making sure the moisture has been wrung out), cottage cheese, pure vanilla extract, and the whole milk.
Blend until the mixture is smooth and combined.
Add the oats to the buttered baking dish. Also, add the baking powder and mix.
Pour the wet ingredients into the baking dish.
Using a utensil that won’t scratch the baking dish, mix the oats with the wet ingredients.
Bake for about 40 minutes. The edges should be golden brown and it might still feel a bit soft to the touch. As it cools, it will firm up some more.