Preheat the oven to 350ºF. Grease a 9 x 13 inch (22 x 33 cm) pan. or line with parchment paper.
Toss chopped apples with sugar and cinnamon. Set aside.
Process chickpeas and eggs in a food processor or blender until smooth and set aside.
In a large mixing bowl, mix coconut oil, apple sauce, and brown sugar until well combined. Add the chickpea mixture and vanilla and beat again. In a medium bowl, stir together whole wheat flour, spelt flour, baking powder, cinnamon, nutmeg, and salt. Add half of the flour mixture to chickpea mixture, and beat until just combined. Add milk, and beat again, then rest of the flour mixture, and beat until just combined.
Spread batter in greased pan. Pour apple mixture evenly overtop, then press into the batter with back of a large spoon until batter just starts to press up through the apples. Bake in the middle of the oven for about 55 to 60 minutes, or until a tester inserted in the center comes out clean. Cool completely before cutting into 18 pieces.
Dust slices with icing sugar before serving.