Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a mixing bowl, combine the rolled oats, flour, baking soda, cinnamon, and salt.

In another bowl, cream together the softened butter, brown sugar, and granulated sugar until smooth.

Beat in the egg and vanilla extract until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the diced apple and chopped walnuts.

Drop spoonfuls of the cookie dough onto the prepared baking sheet, spacing them about 2 inches apart.

Bake in the preheated oven for 10-12 minutes, or until the edges are golden brown.

Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.