Preheat oven to 350°F (175°C) and apply non-stick spray to two 6-cavity donut pans.
In a primary mixing bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and cinnamon until homogeneous.
In a secondary bowl, combine the mashed bananas, eggs, milk, vegetable oil, and vanilla extract, whisking until emulsified.
Incorporate the wet mixture into the dry ingredients, stirring only until no dry streaks remain.
Transfer the batter to a piping bag and dispense into the donut cavities, filling each to approximately 75% capacity.
Bake for 10 to 12 minutes or until the internal temperature reaches 200°F (93°C) and a tester comes out clean.
Cool donuts in the pan for 5 minutes before transferring to a wire cooling rack.
Submerge the surface of each warm donut into melted butter, then immediately press into the cinnamon sugar mixture to coat.