In a saucepan over medium heat, add milk and butter. Stir until melted. Remove from heat.
In a large mixing bowl or stand mixer fitted with the paddle attachment, combine 2¼ cups flour (holding remaining cup back), sugar, pumpkin pie spice and salt on low speed. Pour lukewarm butter and milk mixture over and sprinkle yeast over the top. Stir on low until just combined. Add pumpkin and egg until just incorporated.
Using the dough hook attachment on a stand mixer (or hands), knead dough while gradually adding in the remaining 1 cup of flour, until the dough forms a ball and pulls away from the edges of the bowl.
Let dough rest for 10 minutes. Preheat oven to 350℉.
Fill
On a lightly floured surface, roll dough into a rectangle. Brush melted butter on top. In a small bowl, combine brown sugar, cinnamon, and pumpkin pie spice. Sprinkle on top. Roll sheet of dough. Using a knife or pizza cutter, gently cut into 10 equal rolls. Place in a baking dish or cast iron skillet.
Turn oven off. Cover rolls with a damp towel and place inside warm oven to to rise for 25 minutes. Remove from oven and preheat to 350℉.
Cover rolls in ¼ cup heavy cream. Bake 15-20 minutes, or until slightly golden.
Icing
In a medium mixing bowl, whisk to combine cream cheese, butter, powdered sugar and heavy cream (and optional pumpkin spice seasoning) until smooth. Spread onto rolls or warm to pour over rolls.
Notes
Tips
Use a stand mixer for ease, or you can also knead by hand. Kneading by hand will take about 10-12 minutes and in a mixer it will take around eight minutes.
Want a thinner cream cheese glaze? Just add a little more cream.