Place the pumpkin puree in cheesecloth or several layers of paper towel. Gently drain or press out excess moisture. Set aside.
In a large mixing bowl, cream together the softened butter, dark brown sugar, and granulated sugar until smooth and creamy.
Add the egg yolks and vanilla extract. Mix until fully incorporated.
Add the drained pumpkin puree and mix until combined.
In a separate bowl, whisk together the all-purpose flour, salt, pumpkin spice, and baking soda.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Do not overmix.
Cover the dough and refrigerate for about 30 minutes, or until firm enough to scoop easily.
Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper.
Scoop the chilled dough onto the prepared baking sheets, leaving space between each cookie.
Bake for 10–15 minutes, or until the edges are set and the centers still appear slightly soft.
Allow the cookies to cool on the baking sheet for several minutes before transferring them to a wire rack.
Once completely cooled, drizzle the melted white chocolate over the cookies.
Allow the white chocolate to set before serving.