1. Preheat the oven to 375 degrees. Lightly grease a muffin pan with a non stick spray.
2. In a large bowl mix the flour, bran, sugar, Splenda, baking powder, baking soda, salt, and walnuts. In a small bowl, beat the eggs until they are foamy. Then add apple sauce and vanilla extract.
3. Combine the two mixtures; add in the zucchini and carrots. Stir until it is just blended. Spoon batter into prepared non stick muffin cups, filling them about 3/4 full.
4. Bake for 15-20 minutes, until a toothpick inserted into the center of one muffin comes out clean. Cool in the pan on a wire rack for five minutes. Remove muffins from the rack and allow cooling completely before storing. Muffins are great fresh or they can be frozen for later.