Add the warm milk (105°-110°F), egg, pumpkin, sugar, yeast, salt, spices and 1 cup of flour to the bowl of a stand mixer fitted with the paddle attachment. Mix on low speed until combined. Scrape down the paddle and switch to the dough hook.
With the mixer running on low, add the remaining flour 1/2 cup at a time until the dough begins to pull away from the sides. It will be slightly sticky, but not so much as it sticks to your fingers and leaves dough behind. Knead on low for 2-3 minutes until it all comes together in a smooth, very soft dough.
Transfer the dough to a large, greased bowl and cover with plastic wrap. Let rise in a warm spot until doubled, about 1.5-2 hours.
While the dough rises, prepare the filling by combining the softened butter with both sugars and cinnamon together in a small bowl. Prepare a 9x13 pan by spraying with pan spray and setting aside.
Once the dough has finished rising, turn it out onto a lightly greased surface. Gently roll into a 16x12-inch rectangle. Spread the cinnamon sugar butter across the dough, leaving about a ½-inch border along the top and bottom of the dough.
Roll the long side of the dough up into a tight roll and place with the seam side down. Slice into 12 even rolls. Place rolls in the prepared baking pan and cover with plastic wrap.
Let rise in a warm place for 1 hour, or until doubled in size. When the rolls are nearly doubled in size, preheat the oven to 350°.
Once the rolls are done rising, remove the plastic wrap and bake for 23-25 minutes, until they are a light golden-brown color.
Prepare the frosting by combining the cream cheese, milk, vanilla, and powdered sugar until smooth. Spread over the warm rolls. These rolls are best served warm.