Preheat the oven to 350°F (175°C).

In a mixing bowl, cream together the softened butter, granulated sugar, and brown 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, and salt.

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

In another bowl, combine the flour and brown sugar for the crumble topping.

Add the cold cubed butter and use a fork or pastry cutter to mix until the mixture resembles coarse crumbs.

Stir in the rolled oats until evenly distributed.

Drop spoonfuls of the cookie dough onto a baking sheet lined with parchment paper.

Sprinkle the crumble topping generously over each cookie dough mound.

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

Allow to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.