In a mixing bowl, combine eggs, sugar, oil and vanilla; mix well. Combine dry ingredients; add to the egg mixture and mix well. Batter will be stiff. Stir in apples and walnuts. Spread into a greased 9 x 13-inch pan. Bake at 350° for 45-50 minutes or until toothpick inserted in center comes out clean. Cool on wire rack. Butter Sauce: Combine sugar, flour, milk and butter in saucepan. Bring to a boil over medium heat; boil and stir for 2 minutes. Remove from heat; stir in vanilla. Cut cake into squares; top with warm sauce. Garnish with walnut halves if desired. Yield: 12-15 servings.
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