Preheat the oven to 190 degrees C. Grease a square baking tin, or line with baking paper.
In a large bowl, whisk together the eggs, applesauce, oil, brown sugar and vanilla. Combine the flour, baking soda and cinnamon and stir into the wet mixture until moistened.
Spoon half of the batter into baking tin and spread evenly. Place apple slices on top of mixture and cover with remaining batter.
Bake for 30 minutes in the preheated oven, or until the top of the cake springs back when pressed lightly. Cool before removing from tin and cutting into slices.