In the bowl of a stand mixer, beat melted butter and sugars until thoroughly combined. Add in the vanilla and pumpkin puree and beat until smooth.
In a large bowl, stir together flour, salt, baking powder, baking soda, cinnamon, nutmeg, and allspice. Slowly add the flour mixture to the butter sugar mixture, beating in between each addition (I divided my flour mixture into two additions) until just combined. Stir in the mini chocolate chips. Cover the dough and chill for at least 30 minutes (up to three days maximum).
Preheat oven to 350 degrees. Line two baking sheets with silicone baking mats or parchment paper.
Roll approximately 2 to 2 1/2 Tbsp of dough into a ball, then flatten into a disc. Add one caramel candy to the center and wrap the dough around, pressing the edges closed so it is sealed well. Repeat with the rest of the dough until you have approximately one dozen balls of dough. Bake cookies for 12 to 15 minutes total. The dough will be a bit soft. Remove from oven and allow to cool approximately 5 minutes on the baking sheets before serving. Make sure you serve these warm so you get that ooey-gooey caramel center!