Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large mixing bowl, whisk together the softened butter, granulated sugar, and brown sugar until the mixture is light and fluffy, and the sugars are fully incorporated.
Add the egg to the bowl and beat until the mixture becomes smooth and creamy. The mixture should have a pale, airy appearance and smell sweet.
Stir in the pumpkin puree until well combined, resulting in a slightly thick, orange-tinted batter that smells warmly spiced.
In a separate bowl, sift together the flour, cinnamon, nutmeg, cloves, baking soda, and salt to evenly distribute the spices and leavening agents.
Gradually add the dry ingredients to the wet mixture, folding gently to incorporate everything without overmixing. The dough will become thick and slightly sticky but manageable.
Using a spoon or cookie scoop, portion out the dough onto the prepared baking sheet, leaving enough space for spread. Slightly flatten each mound with the back of a spoon or your fingers.
Bake in the preheated oven for about 12 minutes, or until the edges are golden and the centers look set but slightly soft. The cookies will smell warm and spicy as they bake.
Remove the baking sheet from the oven and let the cookies cool on the sheet for 5 minutes until they firm up slightly, then transfer them to a wire rack to cool completely.
Once cooled, the cookies will have a rustic look with slightly cracked tops and a tender, chewy texture inside, with a fragrant pumpkin spice aroma filling your kitchen.