Beat the eggs with 1 cup of sugar. Add oil and flour with baking powder. From the mixture, set aside 3 tablespoons and pour the remaining mixture in a pre-buttered and floured baking dish.
Grate the apples and crush the walnuts. Combine the apples with the vanilla, cinnamon and 1 cup sugar. Pour the walnuts over the mixture and arrange apples on top.
Mix the set aside mixture with flour, in order to obtain small crumbs. Pour it over the apples.
Bake the cake in a preheated 356°F (180 °C) oven. Finally, sprinkle with powdered sugar.