Warm the milk until lukewarm. Do not overheat it. Pour the milk into a large bowl and stir in the active dry yeast and granulated sugar until dissolved. Let the mixture sit in a warm place until foamy, about 10 minutes.
Add the melted butter and eggs to the yeast mixture. Whisk gently until smooth and combined.
Gradually add the self-rising flour and mix until a soft dough forms.
Transfer the dough to a lightly floured surface and knead for 2–3 minutes, until smooth and slightly tacky.
Place the dough back into the bowl, cover, and let it rise in a warm place for at least 30 minutes, or until slightly puffed.
Preheat the oven to 320°F and line a 9x13-inch baking pan with parchment paper.
Roll the dough into a large rectangle on a lightly floured surface. Spread the pumpkin puree evenly over the dough.
In a small bowl, combine the packed brown sugar, ground cinnamon, and ground nutmeg. Sprinkle the mixture evenly over the pumpkin layer.
Roll the dough tightly into a log and cut into 18 small, 1-inch-thick rolls.
Arrange the rolls evenly in the prepared baking pan. Bake for about 20 minutes, or until the rolls are golden brown and cooked through