Prepare the Oven and Baking Sheets: Preheat your oven to 350°F. Line two baking sheets with parchment paper and set them aside.
Cream the Butter and Sugars: Add the softened butter, brown sugar, and granulated sugar to a large mixing bowl. Beat until smooth, creamy, and well combined.
Add the Wet Ingredients: Add the egg, pumpkin puree, molasses, and vanilla extract. Mix until everything is smooth and evenly incorporated.
Combine the Dry Ingredients: In a separate bowl, whisk together the all-purpose flour, baking soda, pumpkin pie spice, cinnamon, ginger, nutmeg, and salt.
Make the Cookie Dough: Gradually add the dry ingredients to the wet mixture. Mix just until a soft cookie dough forms. Avoid overmixing.
Chill the Dough: Cover the bowl and refrigerate the dough for about 30 minutes, or until firm enough to scoop and shape easily.
Shape the Cookies: Scoop the chilled dough into portions and gently roll each portion into a ball. Roll each dough ball in coarse or granulated sugar until lightly coated.
Bake the Cookies: Arrange the cookie dough balls on the prepared baking sheets, leaving space between them. Bake for 9–11 minutes, or until the edges are set and the centers still look slightly soft.
Cool the Cookies: Let the cookies cool on the baking sheet for several minutes. Transfer them to a wire rack and allow them to cool completely before serving or storing.