Preheat oven to 350°F.
Put apples in medium saucepan with ¼ cup water. Cover and cook 3–4 minutes over medium heat, until soft. Add maple syrup and stir to combine.
In a small mixing bowl, combine flour, baking soda, baking powder, cinnamon, ginger, allspice, nutmeg, and salt. Set aside.
In a separate bowl, mix applesauce, molasses, egg replacers, vanilla, and ¼ cup water. Add to dry ingredients and mix well.
Spread cooked apple-maple syrup mixture evenly on the bottom of a 9 × 9 nonstick baking dish. Pour batter over apples.
Bake uncovered for about 35–40 minutes, or until a toothpick inserted in the center of the gingerbread comes out clean.
While cake is still warm, place a serving plate over cake pan and carefully turn the cake over so it comes out onto the plate. Serve warm.