Preheat the oven to 350°F (175°C) and lightly grease the donut pan with non-stick spray.
In a large mixing bowl, mash the ripe bananas until smooth with a fork or potato masher, ensuring there are minimal lumps.
1 1/2 cups all-purpose flour
Add the melted butter, egg, vanilla extract, and milk to the mashed bananas. Whisk until well combined and the mixture is smooth.
1 1/2 cups all-purpose flour
In a separate bowl, sift together the flour, sugar, baking powder, and salt. Gradually fold these dry ingredients into the wet banana mixture until just combined; do not overmix.
1 1/2 cups all-purpose flour
Spoon the batter into the prepared donut pan, filling each cavity about 3/4 full. Smooth the tops with a spatula or the back of a spoon.
Bake for 12-15 minutes, or until the donuts are golden brown and a toothpick inserted into the center comes out clean. Remove from oven and let cool for a few minutes before transferring to a wire rack.
Mix powdered sugar with 1 tablespoon of milk until smooth and drizzle over the cooled donuts for a simple glaze. Let the glaze set before serving.
1 1/2 cups all-purpose flour