Preheat oven to 350 deg. F. Grease a 9x13” pan. Wash, core, and dice 1 large apple. In a medium mixing bowl, whisk together 1 cup applesauce, 1/2 cup safflower oil, 1/2 cup brown sugar, 1/2 cup maple syrup, 1/4 cup ground flaxseed meal, 1/4 cup arrowroot starch, and 1 tsp. vanilla extract until sugar is dissolved and the mixture is thick and glossy. Mix in 2 cups flour, 2 tsp. baking powder, 1 tsp. ground cinnamon, and 1/2 tsp. salt. Fold in diced apple and 1/2 cup raisins, dried cranberries, or diced crystallized ginger (optional). Scrape batter into prepared pan. Bake 35-40 minutes, until a cake tester can be removed cleanly. Allow cake to cool before frosting.
Mix together 2 cup icing sugar/confectioners’ sugar, 2 TB softened dairy or non-dairy butter, 1/4 TB maple syrup, and 2 tsp. vanilla extract. Frost cake.