Heat the milk until it is warm to the touch. To a large mixing bowl, add the warm milk. Stir in the oil and sugar until the sugar is dissolved. Sprinkle the yeast over the warm milk and sugar mixture and let stand and allow to bloom, 5 minutes. Whisk in the pumpkin puree until smooth.
In another bowl, stir together 4 ups of the flour, cinnamon, ginger, and nutmeg. (Reserve the remaining 1/2 cup flour, baking powder, baking soda, and salt for later). Add the flour and spices to the pumpkin mixture, stirring until a soft dough forms. Cover the bowl with kitchen towel and allow to rise in a warm place, 1 hour. When the dough has risen and doubled in size, stir in the remaining flour, along with the baking powder, baking soda, and salt until incorporated.
Preheat the oven to 375. Grease two 12-inch cast iron skillets or large pie plates. Flour your work surface liberally. Roll the dough out into a large rectangle, about 18 x 24 inches. Using a pastry brush or your fingers, spread the melted butter evenly over the surface of the dough. In a bowl, stir together the sugar, brown sugar, cinnamon, ginger, and nutmeg. Sprinkle the sugar mixture evenly over the melted butter. Starting at the bottom and working upward, roll the dough inward onto itself, sealing the butter and spices inside. Place the roll seam side down and, using a sharp knife, slice it into 1-inch rolls. Place the rolls into the prepared pans, about 6 per pan. Allow to rise 20 more minutes. (At this point if you’d like to freeze a pan for later, cover it tightly and place a pan in the freezer). Bake the rolls for 20-22 minutes, until browned on the edges and set in the center.
While the rolls are baking, cream together the cream cheese and butter in a stand mixer fitted with the whisk attachment on medium high speed. Add the vanilla, orange zest and milk, beating on medium speed until smooth and combined. turn off the mixer and add the powdered sugar. turn the mixer on low, mixing until the powdered sugar in incorporated, then turn it up to medium until smooth, scraping the sides and bottom of the bowl as needed. Spread the frosting onto the rolls as soon as they come out of the oven. Serve the rolls warm.