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

In a large mixing bowl, cream together the softened butter, packed brown sugar, and granulated sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.

In a separate bowl, whisk together the flour, baking soda, ground cinnamon, ground nutmeg, and salt, then gradually mix into the wet ingredients.

Fold in the diced apples until evenly distributed.

For the crumb topping, mix together flour, rolled oats, brown sugar, ground cinnamon, and a pinch of salt, then stir in melted butter until crumbly.

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

Sprinkle the crumb topping generously over each cookie dough ball.

Bake for 12-15 minutes until edges are golden and centers are set.

Cool on the baking sheet for 5 minutes before transferring to a wire rack.