Nanna Shirley...this is from the first edition Betty Crocker's Picture Cookbook from 1950...sounds like it might be the one.

APPLESAUCE CAKE

Applesauce:
Wash, quarter, and core 6-8 tart apples. Add 1/4 cup water. Cover and cook to a mush, stirring occasionally. Press through a sieve of food mill.

Cake:
Grease and flour a 13x9-inch pan.

Cream together until fluffy:
1/2 cup soft shortening
2 cups sugar

Beat in thoroughly:
1 large egg

Stir in:
1 1/2 cups applesauce

Sift together:
2 7/8 cups sifted cake flour or 2 1/2 cups sifted all-purpose flour
1 1/2 tsp. soda
1 1/2 tsp. salt
3/4 tsp. cinnamon
1/2 tsp. cloves
1/2 tsp. allspice

Stir in alternately with:
1/2 cup water

Stir in:
1/2 cup walnuts, cut-up
1 cup raisins, cut-up

Pour into prepared pan.

Bake in 350 degree oven for 45-50 minutes, until cake tests done. Cool.

Dust with confectioner's sugar, if desired.