Proof the yeast: Warm the milk to 105–115°F. Stir in 1 tablespoon of the granulated sugar, sprinkle the yeast over the milk, and let sit 5–10 minutes until foamy.
Mix wet ingredients: In a large bowl, whisk together the eggs, pumpkin puree, melted butter, and the remaining granulated sugar. Add cinnamon and nutmeg.
Make the dough: Add the foamy yeast milk to the wet mixture, then gradually stir in the self-rising flour until a soft dough forms. Turn onto a lightly floured surface and knead 4–6 minutes until smooth and slightly elastic. (If the dough feels too sticky, add flour a tablespoon at a time.)
First rise: Place the dough in an oiled bowl, cover with a damp towel or plastic wrap, and let rise in a warm place for 45–60 minutes, or until doubled in size.
Shape: Punch down the dough, then roll it out into a rectangle about 12 x 18 inches. Brush with a little melted butter if desired. For the filling, mix 2 tbsp brown sugar, 1 tbsp granulated sugar, and an extra ½–1 tsp cinnamon with a pinch of nutmeg. Sprinkle evenly over the dough.
Roll and cut: Roll tightly from the long edge into a log, seal the seam, then cut into 8 equal pieces. Place the rolls cut-side up in a greased baking dish, leaving space between each.
Second rise: Cover and let the rolls rise again for 20–30 minutes while preheating the oven to 350°F (175°C).
Bake: Bake for 25–30 minutes, until golden and fragrant.
Make the frosting: Beat together cream cheese, powdered sugar, pumpkin puree, and milk until smooth.
Frost and enjoy: Spread over the warm rolls and serve immediately for the ultimate fall treat.