Activate the Yeast: Begin by sprinkling the yeast over the warm milk in a small bowl; give it a gentle stir and let it sit for about 3 to 5 minutes to activate.

Mix Dry Ingredients: In a stand mixer bowl, combine the flour, sugar, salt, and pumpkin spice.

Combine Mixtures: When the yeast is frothy, add it to the dry ingredients along with the pumpkin puree and egg. Use the hook attachment to mix on low speed until the dough begins to come together.

Increase the speed to medium-high and knead until smooth and elastic, passing the windowpane test. If the dough is too sticky, gradually add a tablespoon of flour at a time.

Incorporate Butter: Add the softened butter and knead again until fully absorbed.

First Proof: Shape the dough into a ball and transfer it to a lightly greased bowl. Cover and let it proof in a warm area for 45 minutes to an hour, until doubled in size.

Prepare Miscellaneous Tools: While the dough is proofing, prepare two sheet pans and cut 12 small squares of parchment (about 3×3 inches).

Shape the Donuts: Punch down the dough, turn it out onto a floured surface, and divide into 12 equal pieces. Roll each piece into a tight ball.

If keeping them circular, place each ball seam-side down onto a parchment square; to shape them into pumpkins, wrap twine around each dough ball and tie the ends.

Second Proof: Let the shaped donuts proof in a warm, moist area for another 45 minutes to an hour.

Prepare Cinnamon Sugar and Filling: Mix sugar and cinnamon for coating. Blend cream cheese, pumpkin puree, pumpkin spice, and vanilla until smooth, gradually adding powdered sugar and then heavy cream until stiff peaks form.

Heat Oil: Set a pot with 1½ to 2 inches of oil over medium heat, reaching 325°F.

Fry Donuts: Transfer a donut using the parchment paper, remove the paper after a few seconds, and fry each side for 2 to 3 minutes until golden brown.

Coat: Roll the donuts in cinnamon sugar immediately after frying.

Cool and Fill: Allow the donuts to cool for 10 to 15 minutes, then use a chopstick or the back of a spoon to create a filling space in each donut. Pipe in the pumpkin cream until they are generously filled.

Garnish: Optionally, add a cinnamon stick piece to create a charming pumpkin stem for presentation.