Turn oven on to 'keep warm' setting - around 145F.
In a bowl, mix together flour, yeast, sugar, salt, and pumpkin pie spice.
In a microwave safe large bowl, add butter and milk. Microwave for about 1 minute or until butter has softened greatly and milk is warm (but not hot). Whisk together.
Whisk in egg and pumpkin puree.
Using a wooden spoon, add in flour mixture to milk mixture slowly until all incorporated. Dough will be shaggy and take some arm strength to mix. If dough is super sticky to the touch, add more flour.
Knead dough by hand for 5 minutes on a floured surface, you want the dough to be slightly sticky but not enough to stick to your hands so add more flour as needed.
Form into ball and place in bottom of greased large bowl. Cover with plastic wrap and add to warmed oven with door slightly ajar. Alternatively, keep dough in a decently warm place to allow for rising. Let dough rise for 60-70 minutes or until doubled in size.
Once dough has doubled, dump onto floured surface and using a roller, roll out into a 10x14 rectangle. Spread softened butter around the entire surface, leaving about 1 inch perimeter around the edges.
In a small bowl, mix together the brown sugar and the pumpkin pie spice, then add that on top of the butter and press down slightly to pack.
Start rolling tightly from the long side until you have created one log. Using dental floss, slice into 10-12 rolls. Alternatively, use a knife but floss will slice them perfectly without smushing.
Grease a ceramic 9x13 casserole dish and add rolls to dish. Cover with plastic wrap and place back into warm spot for another 60 minutes to rise again.
After 60 minutes, remove from oven and take off plastic wrap. Preheat oven to 350F. Once preheated, bake in oven for 30-32 minutes. Let cool for at least 20 minutes before icing.
While the rolls are cooling, make icing. Using a hand mixer, beat together cream cheese and butter. Beat in vanilla and slowly add powdered sugar. Then beat in salt and pumpkin pie spice.
Spread icing on rolls and enjoy!
