Preheat over to 350 F and grease two 8x8 square pans.
Mash bananas until they're liquid and add vanilla, sugar, oil and applesauce. Mix thoroughly. In a separate bowl, mix flours, baking soda, baking power and ginger and cinnamon. Make a well in the dry ingredients and pour in the wet-; mix well. Add almond milk by 1/4 cup portions until the dough has a slightly elastic but runny consistency. Add cider vinegar, pour into pans, bake for about 25 minutes or until an inserted toothpick comes out clean. Cool on cooling rack.
For icing, melt chocolate chips- one cup or so- in a double boiler and add two or so tablespoons of almond milk. stir to combine. Cool in fridge. Should have a creamy, spreadable consistency. If you want thicker creme, add more chocolate. Thinner, more almond milk. Spread over cooled cakes.