Preheat oven to 425 degrees F. Grease muffin cups.
Mix together wheat bran, yogurt, and buttermilk. Let stand for 10 minutes.
Beat together applesauce, carrot, egg, honey, and vanilla. Add to yogurt bran mixture.
In a separate bowl, sift together flour, baking soda, baking powder, pumpkin pie spice, and salt. Stir flour mixture into bran mixture, until just blended. Fold in walnuts and spoon batter into prepared muffin tins.
Bake in preheated oven for 5 minutes and then reduce heat to 350 for 20 to 25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.