Preheat oven to 425F. Grease an 8-inch or 9-inch round pan with nonstick spray or butter. Set aside.
In a large mixing bowl, prepare dough by combining self-rising flour, pumpkin puree, milk, cream, melted butter, and ground nutmeg. Stir just until ingredients are well-combined.
Turn dough out onto a well-floured surface (I like to flour a piece of parchment paper for easy clean-up). Sprinkle the top of the dough liberally with flour, then dust your hands with flour. Press the dough out into a rectangle about 9x11-inches or so.
Spread softened butter over the surface of the dough (I use my hands for this).
In a small bowl, whisk together brown sugar and cinnamon for the filling. Sprinkle that mixture evenly over the butter layer.
Starting with the long edge of the rectangle, carefully roll the dough tightly into a log. Using a serrated knife, slice off the irregular ends of the log, then divide the remainder of the log into 8 pieces (I cut the log in half, then cut those pieces in half, then cut those in half).
Place sliced rounds into the prepared pan. Drizzle the warmed cream over the rolls, allowing it to drip through the rolls and down into the bottom of the pan.
Bake in preheated oven for about 18-20 minutes, or until tops are golden-brown.
While the rolls are baking, prepare the icing by combining cream cheese, butter, powdered sugar, vanilla extract, cinnamon, and 2 tablespoons of milk in a small mixing bowl. Use an electric mixer to beat until smooth. If the mixture is too thick, add another tablespoon of milk.
Once you remove the rolls from the oven, let them cool for about 5 minutes, then spread the tops with icing. Serve warm and enjoy!