Preheat oven to 350°F / 175°C. Make flax eggs by mixing flax meal and water; let sit for 10-15 minutes. Grease a 9"x9" pan.
In a large bowl, mix flour, baking powder, baking soda, spices, and salt.
In a separate bowl, whisk sugar, oil, applesauce, milk, flax eggs, vanilla, and apple cider vinegar.
Pour wet ingredients into dry ingredients; stir until the batter is mixed. Add nuts and apples.
Pour into the baking pan, spread evenly, and bake for 45-50 min. Rotate the pan once during baking.
Once done, let the cake cool. Meanwhile, whisk glaze ingredients until smooth; pour over the cooled cake.