In a large bowl, sift together flour, baking powder, baking soda, cinnamon, and salt. Stir in bran, carrots, raisins, and nuts.
In a separate bowl, beat honey, milk, oil, and eggs together.
Make a well in dry ingredients; pour liquid mixture in well, mixing until just moistened. Spoon into greased muffin tins, filling each two-thirds full.