Mix eggs, sugar, melted fat and scraped vanilla pulp. Mix flour, cinnamon, salt and baking powder and pour in. Mix to a smooth batter.
Peel the apples, remove the core and grate coarsely. Stir the apples and nuts into the dough. Carefully grease a baking pan and pour in the batter. Bake in a preheated oven at 175 degrees for about 55 minutes. Let cool and sprinkle with powdered sugar.