Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13 inch pan. Cut the apples into 1 inch wedges. Set aside.
In a large bowl, whisk together the eggs and sugar until blended. Mix in the baking soda, oil, cinnamon and vanilla. Stir in the flour, just until incorporated. Fold in the apples and walnuts.
Pour batter into prepared pan. Bake in the preheated oven for 55 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool slightly. May be served warm or at room temperature.
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