Preheat the oven: Begin by preheating your oven to 350°F (175°C). This will ensure that the cookies bake evenly. Line two baking sheets with parchment paper to prevent sticking.
Prepare the cookie dough: In a large mixing bowl, beat together 1 cup unsalted butter, 1 cup granulated sugar, and ½ cup brown sugar using an electric mixer until the mixture is light and fluffy. This usually takes about 3-5 minutes. Next, mix in 1 cup pumpkin puree, 1 egg, and 1 tsp vanilla extract until well combined.
Combine dry ingredients: In a separate bowl, whisk together 2 ½ cups all-purpose flour, 1 tsp baking soda, ½ tsp baking powder, ½ tsp salt, 1 tsp ground cinnamon, ½ tsp ground nutmeg, and ¼ tsp ground cloves. Gradually add the dry ingredients to the wet mixture, mixing until just combined; avoid overmixing.
Make the crumble topping: In a smaller bowl, prepare the crumble by mixing ½ cup all-purpose flour, ¼ cup granulated sugar, ¼ cup brown sugar, ¼ cup cold butter, and ½ tsp ground cinnamon. Use your fingertips or a fork to blend until crumbly.
Form the cookies: Using a tablespoon or cookie scoop, drop rounded balls of dough onto the prepared baking sheets, spacing them about 2 inches apart. Sprinkle the crumble topping generously over each dough ball.
Bake: Place the baking sheets in the preheated oven and bake for 12-15 minutes, or until the cookies are golden brown around the edges. The centers may still look slightly soft, which is normal.
Cool: Once baked, remove the cookies from the oven and let them cool on the baking sheets for about 5 minutes before transferring them to wire racks to cool completely.