Preheat the oven to 350°F (175°C).
In a large mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.
Add the egg and pumpkin puree to the creamed mixture, mixing until combined.
In a separate bowl, whisk together the flour, baking soda, cinnamon, nutmeg, and salt.
Gradually add the dry mixture to the pumpkin mixture and stir until just combined.
Prepare the crumble topping by combining oats, flour, brown sugar, and butter in a bowl until crumbly.
Scoop tablespoons of cookie dough onto a lined baking sheet, spacing them a few inches apart.
Sprinkle the crumble topping generously over each cookie dough ball before baking.
Bake in the preheated oven for 12–15 minutes, or until edges are golden brown.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.
