Preheat oven to 375 degrees F (190 degrees C). Grease 8 muffin cups or line with paper muffin liners.
Stir together 1 cup flour, baking soda, salt and cinnamon. In a separate bowl, cream together brown sugar and applesauce. Beat in egg white and vanilla.
Stir flour into egg mixture alternately with milk. Mix in an additional 1 tablespoon of flour. Fold in chocolate chips and walnuts. Spoon batter into prepared muffin cups so that cups are half full.
Bake in preheated oven for 13 to 15 minutes, until a toothpick inserted into the center of a muffin comes out clean.
