Combine warm milk with sugar and yeast in a small bowl. Gently stir and then let rest for 5 minutes to proof. In the mean time, mix together your pumpkin puree, sugar, egg, and butter in a large mixing bowl.
Add yeast mixture to the wet mixture once proofed. Mix until combined. Then add in the flour, pumpkin pie spice, and salt to the mixture. Fold until a thick dough forms.
Cover with plastic wrap, and chill in the refrigerator for 1 hour. Once the dough has chilled, transfer to a lightly floured surface. Knead for several minutes and then divide into 8 equal portions.
Wrap a piece of thick string around each ball of dough 4 times to create 8 indentations in the dough to give it the pumpkin shape. – Place the dough on a parchment-lined baking sheet.
Heat the oil on the stovetop to 375 degrees over medium heat. Once the oil has reached temperature, fry each dough pumpkin for 3 minutes on each side – or until golden brown. Remove and place on a wire rack. Repeat until all of the doughnuts have been fried.
Preheat the oven to 350 degrees. Prepare the cinnamon and sugar mixture by combining the two in a medium bowl. After the fried donuts have cooled for a couple of minutes, cut the string and remove.
Once all donuts have been coated in the cinnamon sugar, press the cinnamon sticks in the center of each pumpkin for the stem to finish these festive treats.