Preheat oven to 350ºF (177ºC).  Position rack in center of oven.  Line the  muffin pan with paper liners or grease with butter or a vegetable spray.  Set aside. In a small saucepan melt the butter.  Set aside. In a medium sized bowl whisk together the brown sugar, eggs, vanilla extract and mashed banana. Add the melted butter to the brown sugar mixture and stir to combine. In another large bowl combine the flour, baking powder, baking soda, cinnamon, and salt.  Gently fold in the berries, making sure they are coated with flour.  This helps to prevent the berries from sinking during baking.  Do not over mix or the blueberries will end up coloring the batter blue.  Add the wet ingredients to the dry ingredients and stir only until the ingredients are just combined.  Do not over mix the batter or tough muffins will result. Fill each muffin cup about two thirds full of batter, using two spoons or an ice cream scoop.  Fill any unused muffin cups halfway with water to prevent warping of the pan and/or over browning of the muffins.  Place in the oven and bake until a tester inserted in the center of a muffin comes out clean, 20 to 25 minutes. Transfer to a wire rack to cool. Makes 12 regular sized muffins.