Peel and shred apple with cheese grater. Squeeze excess juice and drink or save for later use. Set aside.
In a large bowl beat the butter and sugars until smooth. Add the egg and vanilla. Stir in the flour and spice mixture, oats and apples. Using a two tablespoon scoop place dough on cookie sheets lined with parchment or silicon baking sheet. Bake for 10-12 minutes. Allow to cool on the sheet for 5 minutes and transfer to a rack to cool.
In a small bowl add powdered sugar, maple syrup and milk. Carefully stir to incorporate and drizzle over cookies.
1. I use Honey Crisp apple, feel free to use Granny Smith or other firm apple.