If 18 muffins are too many, freeze those you won't eat and pull them out of the freezer as needed. Warm the muffins slightly before serving.
Heat the oven to 350 F. Line a muffin pan with paper or foil liners.
In a large bowl, combine the flours, sugar, baking soda and cinnamon. Whisk to blend evenly. In a separate bowl, add the egg substitute, oil, applesauce and vanilla. Stir in the apples, raisins and carrots. Add to the flour mixture and blend just until moistened and slightly lumpy.
Spoon the batter into muffin cups, filling each about 2/3 full. Sprinkle with chopped pecans and bake until springy to the touch, about 35 minutes. Let cool for 5 minutes, then transfer the muffins to a wire rack and let cool completely.
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