Place butter, pumpkin puree, brown sugar, and granulated sugar in the bowl of a strand mixer fitted with the paddle attachment. (You can also use a hand mixer.) Mix until combined.
Continue mixing and add the egg yolk and vanilla extract. Add the baking soda, salt, nutmeg, cinnamon, ginger, and allspice and mix until combined, scraping the sides of the bowl as needed.
Slowly mix in flour until a smooth dough forms.
Scoop 1 tablespoon sized balls onto a cookie sheet covered with wax or parchment paper. They don’t need to be far apart, this is for chilling. Chill 30 minutes or until you can easily touch them but they’re still soft enough to roll.
Sandwich the caramel candies between two balls of dough and roll into a large ball.
Stir together 1/4 cup granulated sugar and 1 tablespoon cinnamon in a small bowl. Roll each cookie dough ball in the cinnamon sugar and place back on the cookie sheet. Chill at least one more hour.
Preheat oven to 350°F. Spread cookies onto 2 lined cookie sheets and bake for 12-15 minutes, until the tops are no longer shiny and the bottoms just start to turn brown. Let cool completely before removing.
Store in an airtight container for up to 3 days or freeze for up to one month.