Gently warm the milk until it’s just above room temperature. In a small bowl, mix it with the yeast and granulated sugar. Give it a stir and let it rest in a warm place for about 10 minutes. You’ll know it’s ready when it looks bubbly and foamy on top.
In a large mixing bowl, combine the melted butter and eggs. Pour in your activated yeast mixture and whisk everything together until the texture is smooth and silky.
Gradually stir in the self-rising flour, cinnamon, nutmeg, and brown sugar. Once it becomes too thick to mix with a spoon, transfer the dough onto a floured surface. Knead gently with your hands for 2–3 minutes until the dough is soft, smooth, and springy. Pop it back into your bowl, cover with a kitchen towel, and let it rest somewhere warm for about 30 minutes, or until it doubles in size.
Once the dough has risen, dust your surface with flour and roll the dough into a large rectangle. Spread the pumpkin puree over the surface like you’re icing a giant pumpkin-flavored cookie.
In a separate bowl, stir together some brown sugar, cinnamon, and nutmeg. Sprinkle this spiced sugar mix evenly over the pumpkin layer.
Starting from one of the longer sides, roll the dough up into a tight log. Use a sharp knife or unflavored dental floss to slice the log into 1-inch thick rolls. (Floss gives super clean slices with no squishing!)
Line a 13×9-inch baking pan with parchment paper. Arrange the rolls in the pan, leaving just a bit of space between each one to give them room to puff up. Bake in a preheated oven at 320°F (160°C) for 20 minutes, or until they’re golden brown and your kitchen smells like a fall dream.
While the rolls are baking, make the frosting. In a small bowl, beat together the cream cheese, powdered sugar, pumpkin puree, and milk until smooth and creamy. If it’s too thick, add a tiny splash of water to loosen it up to your liking.
Once the rolls are out of the oven and still warm (but not piping hot), spread the frosting generously over the tops. Let it sit for 5–10 minutes to melt slightly into all those swirls. Finish with a dusting of cinnamon on top for a little extra fall flair.