Preheat the oven to 400 degrees. Wash the apple, cut it into quarters, then cut off the core from each piece. Use a box grater or large holed cheese grater to shred the apple.
In a medium bowl, whisk together the egg, apple sauce, lemon juice, sugar, and shredded apple.
In a separate large bowl, stir together the flour, salt, baking powder, cinnamon, and ginger. Once combined, add the butter and work it into the flour until it resembles coarse, damp sand.
Finally, pour the bowl containing the apple egg mixture into the large bowl with the flour and butter. Stir just until a dough forms and no more dry flour remains on the bottom of the bowl.
Turn the dough out onto a lightly floured surface and shape into a 6-8 inch wide, 1.5 inch thick disc (sprinkle more flour on your hands and on the surface of the dough if needed. The dough may be slightly sticky). Cut the disc into eight wedges.
Line a baking sheet with parchment paper and place the cut scones on top. Bake the scones for 18-20 minutes in the fully preheated oven, or until they are just slightly golden brown on top. Allow the scones to cool completely.
To make the glaze, stir together the powdered sugar, cinnamon, and water until a thick paste forms. Once the scones are fully cooled, drizzle the glaze over top.