Preheat oven to 350℉ (170℃).
Line muffin tins with paper liners or grease and flour them.
Beat the eggs in a large bowl.
Add brown sugar and oil; mix well.
Mix in the bran, cinnamon and ginger. Let the mixture stand for 10 minutes.
Meanwhile, sift together the flour, bicarbonate of soda, cream of tartar and salt.
Add flour mixture to the bran mixture alternately with the buttermilk, stirring well between each addition.
Gently fold in the orange rind, grated carrot and the walnuts.
Spoon mixture carefully into muffin tins, filling them about half full.
Bake for 15 to 20 minutes, until a skewer inserted in the middle of a muffin comes out without any batter clinging to it.
Remove the muffins from the pan and cool on a wire rack.
Serve warm or at room temperature. These are delicious with butter and/or jam. If muffins have cooled to room temperature, you can reheat them in the microwave for about 10 to 15 seconds on high. I sometimes put them frozen in a lunch box and they thaw in time for lunch while helping to keep everything else cool too.