Preheat oven to 350 degrees. Line cookie sheets with parchment paper or silicone baking mat. In a small bowl, whisk together flour, baking soda, salt, cinnamon and nutmeg and set aside.

In a large bowl, cream the butter and sugar until fluffy and light, about 2 minutes.
Add eggs, one at a time, mixing well after each addition. Add vanilla, mix well.

Gradually add the dry ingredients, and mix just until incorporated. Stir in oatmeal. Peel and chop apple, stir into batter.

Using a cookie dough scoop divide dough. You may need to roll in your hands to form a ball. Slightly flatten before baking if you are going to frost the cookies.