Preheat the oven to 190°C (375°F). Line a 12-cup muffin tin with paper liners or grease each cup well.
Peel and mash the bananas in a large bowl until nearly smooth, with only a few small lumps.
Add the eggs, melted butter, milk, vanilla, and sugar to the mashed banana. Whisk until the mixture is uniform and the sugar begins to dissolve, about 60 seconds.
Scatter the flour, baking soda, baking powder, salt, and cinnamon over the wet mixture. Fold gently with a rubber spatula using wide strokes just until no dry flour streaks remain. Do not overmix.
Divide the batter evenly among the 12 muffin cups, filling each about three-quarters full.
Bake on the center rack for 20 to 22 minutes, rotating the tin at 11 minutes. The muffins are done when the tops are golden, spring back when pressed, and a toothpick inserted in the center comes out clean.
Cool in the tin for 5 minutes, then transfer to a wire rack.