In a large mixing bowl, cream butter and brown sugar until fluffy. Add bananas, milk, vanilla, and eggs; blend well. Stir in flour, bran, baking powder, salt, and soda. Stir in chopped pecans. Spoon banana muffin batter into greased or paper-lined muffin cups. Bake at 375° for 20 to 25 minutes, or until a wooden pick or cake tester inserted in center comes out clean. Cook 5 minutes; turn out onto racks to cool completely.
Makes 1 dozen banana muffins.