Preheat oven to 400 degrees F/200 degrees C.
In a large mixing bowl, beat the oil with the sugar and applesauce. Add eggs. In a separate bowl, mix together mix together the flours, baking soda, cinnamon and salt. Add to the liquid ingredients. Fold in grated carrots, grated zucchini and chopped walnuts. Spoon into muffin cups filling 3/4 full. Bake in preheated oven for 20 to 25 minutes or until done when tested with a toothpick. Cool on a wire rack.
For frosting, beat the softened cream cheese with the confectioners' sugar. Add lime juice. Frost the cupcakes with a blunt knife.
Makes 12 cupcakes.
Date: May 29, 2007