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Preheat the oven to 350 degrees.
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Spray a 9-by-13-inch baking pan with nonstick cooking spray and set aside.
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Place the walnuts on a baking sheet and toast in the preheated oven for about 8 minutes, or until they are lightly browned.
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Remove the nuts from the oven and set aside.
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Watch them carefully, as they burn easily.
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In a large bowl, combine the sugar, applesauce, egg, egg white, canola oil and vanilla and mix well.
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In another bowl, combine the flour, salt, baking soda and cinnamon.
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Add the dry ingredients to the wet ingredients and mix well.
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Fold in the apples and toasted walnuts.
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Pour batter into the prepared pan.
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(It will seem like there are more apples than batter, but that's the way it's supposed to look.) Bake in the preheated oven for 50 minutes to 1 hour, or until a golden brown.
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Remove from the oven and allow to cool completely on a rack.
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While the cake is baking, make the frosting.
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Combine the cream cheese, light butter and powdered sugar in a bowl and blend until smooth.
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When the cake is completely cool, spread the frosting evenly over the top.