Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, whisk together the melted butter, granulated sugar, and brown sugar until smooth and well combined. Add the egg and mix until fully incorporated.
Stir in the flour, rolled oats, baking soda, cinnamon, and salt until a soft dough forms. Gently fold in the diced apple.
In a separate small bowl, combine the flour, brown sugar, cinnamon, and a pinch of salt for the crumble topping. Pour in the melted butter and mix with a fork until the mixture becomes crumbly.
Scoop tablespoon-sized portions of cookie dough (we used a cookie scoop) onto the prepared baking sheet, leaving space between each one. Sprinkle a spoonful of the crumble topping over each cookie.
Bake for 12 to 15 minutes, or until the edges are lightly golden and the tops look set.
Let the cookies cool completely on the baking sheet before moving them: they’ll be too soft to handle while warm, but will firm up beautifully as they cool.