Add the warm milk, yeast, and 1 tablespoon of the granulated sugar to a large mixing bowl. Stir gently and let sit for 5 to 10 minutes, until foamy.
Add the remaining sugar, pumpkin puree, egg, and melted butter. Mix until combined.
Add 4 cups of flour, cinnamon, pumpkin pie spice, and salt. Mix until a shaggy dough forms.
Knead with a dough hook on medium-low speed for approximately 6 to 8 minutes. If kneading by hand, transfer the dough to a lightly floured surface and knead until smooth and elastic.
If the dough remains extremely sticky after kneading for several minutes, add additional flour 1 tablespoon at a time. Avoid adding more than necessary.
Transfer the dough to a lightly greased bowl. Cover and let rise in a warm area for 60 to 90 minutes, or until approximately doubled in size.
Meanwhile, prepare the filling by mixing the softened butter, brown sugar, cinnamon, pumpkin pie spice, and salt until combined.
Lightly grease a 9 x 13-inch baking dish.
Turn the risen dough onto a lightly floured surface. Roll into approximately a 14 x 18-inch rectangle.
Spread the cinnamon filling evenly over the dough, leaving about 1/2 inch uncovered along one long edge.
Starting with the opposite long edge, using a pizza cutter, cut long strips about 1-inch wide. Roll from one side of the strip to the next.
Pinch the seam gently closed.
Arrange the rolls in the prepared baking dish. I use two dishes for this.
Cover and let rise for another 30 to 45 minutes, or until visibly puffy.
While the rolls complete their second rise, preheat the oven to 350°F.
Pour heavy cream, if using, over the tops of the cinnamon rolls. Bake for 24 to 30 minutes, until lightly golden and cooked through in the center. If necessary, loosely cover the top with foil toward the end of baking to prevent excess browning.
Remove from the oven and allow the cinnamon rolls to cool for 5 to 10 minutes.
To make the frosting, beat the softened cream cheese and butter until smooth.
Add the powdered sugar, vanilla, and salt. Beat until creamy.
Add milk or heavy cream 1 tablespoon at a time until the frosting reaches your preferred consistency.
Spread the cream cheese frosting generously over the warm pumpkin cinnamon rolls.
Serve warm.