This is a very dense, moist, cake that gets most of its fat from mayonnaise. Be sure to use regular and not low fat. I would not recommend leaving out the nuts or any component of this cake. It needs everything, especially since it doesn't have any butter.
Preheat oven to 350 degrees F. Grease and flour 2 9-inch round cake pans. For extra insurance, you may want to grease, line with parchment then grease and flour again. This is a sticky cake.
In a large mixing bowl, stir together all of the dry ingredients (Flour through cloves).
Add the milk, mayonnaise and eggs and beat with a mixer at low speed beat for 2 minutes, scraping bowl frequently, or beat vigorously 300 strokes by hand. The batter will be thick -- very thick.
With a spoon or heavy duty scraper, stir in apples, raisins and nuts. Spoon batter into pans, dividing evenly.
Bake for 45 min or until tester inserted in center comes out clean. Let cool in pans 10 minutes. Loosen cake from the side of the pan with a knife and remove.
Frost with any kind of light whipped cream frosting or something like a Sea Foam or Seven Minute. The recipe below is what I used in the photo.
Whipped Cream Frosting
Chill the mixing bowl and the whisk attachment of a stand mixer.
Beat the softened cream cheese until light and creamy. Add the powdered sugar, salt and vanilla and beat until smooth and creamy.
With the mixer on low, stream in the heavy whipping cream, beating until incorporated. Increase to medium speed and beat until light and creamy. Keep an eye on it so that it doesn't go from creamy to curdled. Also, taste test and make sure you are happy with the amount of powdered sugar. You may want it a little sweeter.
To frost the cake, spread 1 cup of frosting over the first layer and a second cup of frosting over the top layer. Leave the sides blank or frost the whole thing. Dust cake with cinnamon if desired.