Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper, if desired.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes using an electric mixer.
Add the pumpkin puree and vanilla extract to the creamed mixture, mixing until well combined.
In another bowl, whisk together the instant vanilla pudding mix, flour, baking soda, cinnamon, nutmeg, ginger, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. If using chocolate chips or nuts, fold them in at this stage.
Use a cookie scoop or spoon to drop rounded tablespoons of dough onto the prepared baking sheet, leaving space between each cookie.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden, and the tops look set.
Remove from the oven and allow to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Optional: For a fun twist, try adding a sprinkle of powdered sugar on top before serving.