Warm the milk until it’s just lukewarm - not hot. Stir in the dry yeast and granulated sugar, and let the mixture sit in a warm place for about 10 minutes, until foamy.
Whisk the melted butter and eggs into the foamy yeast mixture. Gradually stir in the self-rising flour, mixing until a dough starts to form.
Dust a clean surface with flour and knead the dough for 2–3 minutes until smooth. Place it in a lightly greased bowl, cover, and let it rise in a warm spot for 30–40 minutes.
Roll out the dough into a rectangle.
Spread pumpkin purée evenly over the surface.
In a small bowl, mix brown sugar, cinnamon, and nutmeg.
Sprinkle this mixture over the pumpkin.
Starting on the long edge, roll the dough into a log. Cut into 1-inch slices using a sharp knife or dental floss for clean cuts.
Line a 13x9-inch pan with parchment paper. Arrange the rolls cut-side up in the pan. Bake at 320°F for about 20 minutes, or until golden brown and puffed.
Whisk together cream cheese, pumpkin purée, powdered sugar, and milk until smooth. Add a little water if needed to thin it out.
Spread the frosting over the warm rolls right out of the oven. Let it set for 5–10 minutes, then sprinkle with cinnamon and enjoy.