Preheat oven to 375 F. Line 12 muffin cups with liners, or spray with baking spray.
In a large bowl, combine flour, baking powder, baking soda, and salt; set aside.
Peel bananas. In another bowl, mash bananas and brown sugar together until relatively smooth.
Add eggs, milk, melted butter, and vanilla, stir until well combined.
Add banana mixture and walnuts to the flour mixture, stir just until moistened (batter should be lumpy.) Divide batter between 12 prepared muffin cups, filling each to almost full.
Bake in a 375 degree F oven for 18 to 20 minutes or until golden and a wooden toothpick inserted in centers comes out clean.
Cool in muffin cups on a wire rack for 5 minutes.
Remove from muffin cups; serve warm.