Preheat oven to 350°F. Line a sheet pan with parchment paper.
In bowl, combine the oats, flour, baking soda, baking powder, cinnamon and salt.
In a separate bowl, beat together the melted butter, brown sugar, and sugar with a wooden spoon until combined. Add the egg and applesauce and mix until combined. Add the dry ingredients, and mix until just combined, then stir in the dried apple.
Drop by the rounded tablespoon onto the prepared sheet pan and bake until edges are just turning golden brown, about 13-15 minutes. Let cool on the pan for 5 minutes, then transfer to a cooling rack to cool completely.
To make the icing, whisk together the powdered sugar and maple syrup. Add enough milk to get the right consistency. Drizzle over the cooled cookies and let set for 10 minutes before serving.