Preheat the oven to 350 degrees.

Combine the first 5 (dry) ingredients in a mixing bowl and stir together. Make a well in the center and pour in the applesauce, oil, and rice milk, stir until well combined, adding more rice milk as needed to make a smooth, slightly stiff batter.

Fold in the walnuts, then divide the batter among 12 lightly oiled or paper-lined muffin tins. Bake for 20 to 15 minutes, or until the tops are golden and a toothpick inserted into the center of one tests clean.

Cool on a rack, then store in an airtight container as soon as the muffins are at room temperature.