Preheat oven to 425°F. Coat 12 muffin cups with cooking spray.
Whisk flour, bran cereal, baking soda, cinnamon and salt in a large bowl. Stir in dates and walnuts. Whisk egg, applesauce, brown sugar and oil in another bowl until smooth. Make a well in the dry ingredients; add the wet ingredients and stir with a rubber spatula until just combined. (Do not overmix.) Spoon the batter into the prepared muffin cups.
Bake the muffins until the tops are golden brown and spring back when touched lightly, 12 to 15 minutes. Let cool in the pan for 5 minutes. Loosen edges and turn muffins out onto a wire rack to cool.