In a large saucepan at medium heat, pour in the milk, vegetable oil, and sugar. Stir until the sugar has dissolved and the milk is "scalded" (very warm but not boiling). Remove from the heat and allow the mixture to cool until the temperature has reached between 95-105 degrees F.
Sprinkle in the active dry yeast and allow the mixture to sit for 5 minutes. Stir in 1 cup of the pumpkin puree. Add in 4 cups of the flour, cinnamon, nutmeg, and allspice and stir until just incorporated. Drape a towel over the pot and allow the mixture to sit in a warm, draft-free place for about 1 hour or until the dough has puffed up.
Add in the remaining 1/2 cup of flour, baking powder, baking soda, and salt. Stir until combined.
After you've made the dough, preheat the oven to 375 degrees F and butter your baking trays.
Turn the dough out onto a lightly floured surface and roll into a large rectangle measuring approximately 10x30 inches.
Spread on the melted butter and remaining 1/2 cup of pumpkin purée. Sprinkle the brown sugar, cinnamon, nutmeg, and pumpkin pie spice on top. Tightly roll the long edge of the rectangle, pinch the seam closed, and turn the log so the seam is facing down.
Cut the rolls into 1/2 inch slices and place them in the prepared pans. Allow the rolls to rise for another 20 minutes or until they are puffed and have spread out.
Place them in the preheated oven and bake for 14-18 minutes or until the edges are golden brown. Spread on the frosting while the cinnamon rolls are warm from the oven, or individually frost once they have cooled.