Spread the walnuts in a shallow baking pan and toast for about 5 minutes, or until fragrant. Remove from the oven and cool.

In a large mixing bowl, whisk together the flour, bran cereal, baking soda, cinnamon and salt. Stir-in the raisins and toasted walnuts.

In another mixing bowl, whisk together the egg, applesauce, brown sugar and oil until smooth and thoroughly combined. Add the egg mixture to the dry ingredients and stir to blend. Do not over-mix.

Divide the batter among the prepared muffin tins and bake for about 15 minutes, or until the top of a muffin springs back when touched lightly. Loosen the edges of the muffins with a small kitchen knife and turn them out onto a wire rack to cool.