Mix dough: In mixer bowl, stir yeast into milk. Add sugar, egg, pumpkin purée, spices, half the flour, and butter. Mix to a sticky mass. Add salt and remaining flour; knead until smooth, stretchy, and slightly tacky (10–15 min by mixer). Rest 20 minutes.
Make filling (optional): Beat cream cheese, brown sugar, pumpkin purée, and spice until smooth. Chill briefly.
Portion: Divide dough into 17 pieces. Flatten, add 1 tsp filling (if using), pinch to seal, and round into balls.
Tie: Arrange four lengths of twine in a crisscross. Set a dough ball seam-down in the center. Tie strings loosely to create pumpkin “ridges.” Place on parchment-lined sheets (about 6 per sheet).
Proof: Cover and rise at room temperature until puffy, 2–3 hours.
Bake: Heat oven to 200°C / 395°F (use 400°F if needed). Bake 10–15 minutes until deep golden. Cool until warm, then snip and remove strings.
Finish: Melt butter. Mix sugar and cinnamon in a shallow bowl. Brush each bun generously with butter, then spoon cinnamon sugar over all sides and into creases. Insert a small piece of cinnamon stick as a stem.
Serve: Best slightly warm. Store airtight (see notes).