Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a mixing bowl, cream together the butter and brown sugar until light and fluffy.
Add the egg and vanilla extract, and mix until well combined.
In another bowl, whisk together the flour, oats, baking soda, cinnamon, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the chopped apple.
Drop spoonfuls of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are golden brown.
Allow cookies to cool on the baking sheet for a few minutes before transferring to a cooling rack to cool completely.