Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats. Set the butter out ahead of time so it's fully softened before mixing.
In a large mixing bowl or stand mixer, beat softened butter with brown sugar and granulated sugar on medium speed for about 2 minutes, until pale and fluffy. Scrape down the sides of the bowl.
Add canned pumpkin puree, egg, and vanilla extract to the butter mixture. Beat on medium speed until fully combined, about 1 minute. The mixture may look slightly curdled, which is normal.
In a separate bowl, whisk together all-purpose flour, baking soda, cinnamon, nutmeg, ginger, cloves, and salt. Whisking the spices into the flour first spreads them evenly.
Add the dry ingredient mixture to the wet ingredients in two batches, mixing on low speed after each addition. Mix just until the flour disappears into the dough.
Fold in old-fashioned rolled oats by hand using a spatula. If using, fold in chopped walnuts or pecans and raisins or mini chocolate chips. The dough will be thick and slightly sticky.
Use a cookie scoop to portion dough into balls of about 2 tablespoons each, spacing them 2 inches (5 cm) apart on prepared baking sheets. Flatten each ball slightly with the back of a spoon or your palm.
Bake for 11 to 13 minutes, until the edges are set and lightly golden while the centers still look slightly soft. Rotate the baking sheets halfway through if your oven runs unevenly.
Let the cookies rest on the baking sheet for 5 minutes before moving them to a wire cooling rack. This short rest lets the cookies firm up enough to transfer without breaking apart.