Brown the butter in a small saucepan over medium heat until it turns a deep amber color. Allow it to cool while you assemble the rest of the wet ingredients: mash three large overripe bananas, about 1c total. Add two eggs, honey, and vanilla, then mix in the cooled brown butter.
Pour the wet ingredients into your bread pan, and add the dry ingredients on top: flour, salt, cinnamon, baking powder, and baking soda.
Set your bread machine to the quick bread setting, light crust. As it starts mixing, scrape the sides and corners with a rubber spatula to ensure all the dry ingredients get combined. Let your machine do the rest! Allow your loaf to fully cool before slicing.