Preheat the oven to 190C/375F/Gas 5 and grease a muffin tin or line with muffin cases.
In a large mixing bowl, cream the butter and brown sugar until fluffy. Add the bananas, milk, vanilla and eggs and mix well.
Combine the flour, bran, baking powder, baking soda and salt and blend into the banana mixture. Stir in as many walnuts as you desire and pour the mixture into the muffin tray or cases.
Bake for 20-25 minutes or until a toothpick inserted into the centre of the muffin comes out clean. Cool in the tray for five minutes then place on a wire rack to cool completely.
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