Preheat oven to 400°F. Lightly oil a 6-muffin tin.
Mix first 4 dry ingredients. Add walnuts and fennel and stir well.
For the liquid ingredients: Combine apple juice with 3/4 cup water and 3 TB canola oil. If using Egg Replacer, warm 2 tablespoons water and throughly mix in the Egg Replacer. Add the mixed Egg Replacer to the apple juce mixture and stir well.
Combine dry and liquid ingredients stirring just enough to thoroughly blend batter. Add more bran if consistency is too thin. Scoop into muffin tin. Bake for 20 minutes. Remove from oven and allow to sit in the tin for a few minutes before removing.