Preheat oven to 350 degrees and line muffin pans with 18 paper baking cups. In a medium mixing bowl stir together flour, baking soda, and salt, set aside.
In a large mixing bowl stir together brown sugar, oil, applesauce, soymilk, vanilla, and bananas. Mix in flour mixture just until blended (do not over mix!). Stir in chocolate chips and walnuts.
Divide batter between baking cups. Bake until a toothpick inserted into the center comes out clean, 25 to 30 minutes. Cool muffins in pans for 10 minutes then transfer to cooling racks to cool completely.