Preheat oven to 350.
Combine butter and both sugars in bowl of stand mixer.
Mix on speed 2 for 4 minutes.
Add eggs, one at a time, mixing until incorporated, scraping sides, if necessary.
Add vanilla, baking soda, salt, cinnamon, and flour, mixing until combined.
Add oatmeal and apple to dough, stirring until combined.
Scoop heaping teaspoon of dough onto parchment paper-lined tray.
Bake for 7 minutes.
Combine 1/3 cup sugar and 2 tsp. cinnamon in a small bowl.
Sprinkle a small amount on each cookie.
Bake for another 7 minutes.
Allow to cool for 2 minutes on tray, then transfer to baking rack to cool completely