Adjust oven rack to middle position and heat oven to 200 degrees. When oven reaches 200 degrees, shut off.
In the bowl of a stand mixer combine the water and sugar; add yeast and let rest 10 minutes until foamy.
Add milk, egg, pumpkin, butter, flour, brown sugar, salt, cinnamon, pumpkin pie spice, ginger, and cardamom to the yeast mixture and mix with the dough hook on medium-low until thoroughly combined, about 5 minutes
Transfer the dough to a lightly oiled bowl, cover with plastic wrap and place in warm oven. Let rise until doubled in size, about 1 hour.
After the dough has doubled in size turn it out onto a lightly floured surface, cover and let rest for 10 minutes.
To make the filling, in a small bowl combine sugars, cinnamon, pumpkin pie spice, allspice, ginger, nutmeg, and cloves; set aside. Line 9×13 inch baking pan with parchment paper, allowing excess to hang over pan edges. Butter the parchment.
Roll dough into a 16×12 inch rectangle. Spread dough softened butter, leaving a 1/4″ margin at the long side of dough. Sprinkle evenly with filling mixture. Use the rolling pin to roll over the filling mixture a few times. Roll up the dough tightly, under-tucking after each completed rollover (it stretch to about 20″ long as you roll). Cut into 15 rolls. Place rolls into prepared 9×13 inch baking pan. Cover and let rise until nearly doubled, about 45 minutes. Meanwhile, preheat oven to 375 degrees F.
Bake rolls in preheated oven until golden brown, about 20-25 minutes.
While the rolls are baking, make the icing by beating together cream cheese, butter, confectioners’ sugar, vanilla extract and salt in the bowl of a stand mixer fitted with the paddle attachment.
Once finished baking flip the pan over to allow all of the cinnamon drippings to recoat the rolls, let sit 1-2 minutes. Turn rolls back over and spread with half of the icing, let sit 2-3 minutes and then spread with remaining icing.