In the bowl of a stand mixer fitted with a paddle attachment, combine the butter, pumpkin puree, brown sugar, and granulated sugar; blend until smooth. Add the egg yolk and vanilla extract and continue mixing until incorporated. Sprinkle in baking soda, salt, nutmeg, cinnamon, ginger, and allspice, mixing thoroughly and scraping down the bowl as needed. Gradually add the flour and blend until a cohesive dough is formed.

Scoop out tablespoon-sized portions of dough onto a parchment or wax paper-lined baking sheet. Arrange them closely together as they will be chilled, not baked yet. Chill for about 30 minutes or until firm but pliable.

Flatten two dough balls slightly, encase a caramel candy between them, and roll into a single, smooth sphere. In a small bowl, mix the remaining granulated sugar with the ground cinnamon for rolling. Coat each filled dough ball in this mixture and return to the baking sheet. Chill for at least another hour to set.

Preheat the oven to 350°F (175°C). Space the cookies evenly across two parchment-lined baking sheets. Bake for 12 to 15 minutes until the tops lose their gloss and the edges begin to brown. Allow cookies to cool fully on the pan before removing.