In a large mixing bowl, combine the apples and sugar; mix well. (Actually I do this as I'm slicing them, so that the sugar keeps the apples from getting dark.)
Stir in oil, nuts, eggs and vanilla; mix well.
Combine dry ingredients and add to apple mixture. Blend well to ensure that you won't have little pockets of flour in the finished cake.
Spoon into a 9x13 pan that has been sprayed with cooking spray.
Bake for 50 minutes to 1 hour at 350° (325° if you use a pyrex pan). It's important not to overcook this cake, so check it at the lower baking time. The center should be just barely set and the edges still fairly soft.
Cool in pan before cutting.
Cut with a sharp knife so that you cut through the apples, rather than dragging half of a slice from an adjacent piece of cake.
You'll probably need something like a pancake turner to get the slices out, especially the first few.
This cake doesn't come out in nice, neat slices, but it tastes wonderful.