Preheat oven to 350 degrees. Line baking sheet with silicone baking mat or parchment paper and set aside.
In a large bowl, cream butter and sugars together until light and fluffy. Stir in egg and vanilla. Slowly incorporate all dry ingredients.
Stir in oats and apples.
Scoop onto prepared sheet.
Bake 8-10 minutes or until the edges are golden.
While cookies are baking, place 1/4 cup butter into small saucepan. With heat on medium, melt and brown the butter. Once the butter is a medium brown/amber color remove from heat and pour into a small bowl.
Stir in powdered sugar and enough milk to get a spreadable consistency.
Frost warm cookies and sprinkle with more cinnamon, if desired. Serve.