Line 18 large muffin cups with paper liners. (This step is important. Do not eliminate the liners.) Sift the flour, sugar, baking powder, baking soda and salt into the bowl of an electric mixer fitted with a paddle attachment. On low speed, incorporate the dry ingredients for about 10 seconds, then add the cooled butter and blend. Combine the eggs, milk, vanilla, and mashed bananas, and add them to the mixture. With a spatula or spoon, blend well but do not overmix.