Preheat oven to 350°F. Line muffin pan with baking cups; set aside.
In a large mixing bowl, whisk together the flour, baking soda, baking powder and salt.
In a medium mixing bowl, beat the eggs and sugar together with a whisk until light and fluffy. Slowly pour in the melted butter in a thin stream, while constantly whisking. Stir in the mashed bananas and vanilla.
With a wooden spoon, make a well in the center of the dry ingredients and pour in the wet ingredients. Gently stir until JUST combined. Evidence of dry crumbs is fine.
Evenly divide batter among 24 muffin cups, filling about 2/3rds full. I like to use my cookie scoop to make this easy.
Bake for 18 to 20 minutes, until toothpick inserted in center comes out clean. Rotate pans halfway through baking time.
Let cool 5 minutes in pan, then immediately remove to wire rack to cool completely.
Store leftovers in a sealed container lined with paper towels for up to 3 days. See notes in the blog post for storing tips.
To freeze, place in single layer in freezer bag. Freeze up to 1 month.