Preheat oven to 400 degrees. Line a baking sheet with parchment paper or a silicone baking mat.
In a mixing bowl, whisk together the flour, sugar, baking powder, and 1 teaspoon cinnamon. Cut the butter into the mixture, using a pastry cutter or two knives, until the mixture resembles a coarse meal with some large chunks of butter. Add the grated apple and stir to coat the apples with flour.
Combine the egg yolk with the milk, pour into the flour mixture, and mix.
Flour a work surface and dump the dough onto it. Knead the dough 2 -3 times, then pat or, using a floured rolling pin, roll the dough out to ½-inch thick. Using a 3-inch biscuit or cookie cutter, cut the scones and place on the prepared baking sheet two inches apart.
In a small bowl, whisk the egg white with 1 tablespoon of water. Brush on top of the scones. Bake for 20 – 22 minutes or until firm to the touch. Let cool in the pan.
Combine the powdered sugar with 1 teaspoon ground cinnamon and 3 tablespoons heavy cream, stir until smooth. Drizzle onto the cooled scones.