MAKE THE DOUGH- In a large saucepan, combine 1 1/2 cups whole milk, 1/2 vegetable oil, and 1/2 cup sugar. Heat until hot but not boiling, then remove the pan from the stove and allow it to cool until the mixture is warm to the touch but not too hot. Sprinkle the yeast over the surface of the liquid and allow to sit for 5 minutes. Stir in pumpkin puree until combined. Combine 4 cups of flour with 1/2 teaspoon cinnamon, 1/4 teaspoon nutmeg, and 1/4 teaspoon ginger. Sprinkle it into the saucepan and stir until it just comes together. Cover the saucepan with a dish towel and set in a warm, draft-free place for 1 hour. After 1 hour, the mixture should be very puffy and at least doubled in size. Stir in 1/2 cup flour, baking soda, baking powder, and salt until totally combined.
MAKE THE ROLLS- Turn out dough onto a floured surface and press it into a rectangular shape. If it is overly sticky, sprinkle generously with flour and handle it/flour it until it\'s easier to handle. Flour a rolling pin and roll the dough into a large rectangle about 10 inches by 30 inches. Drizzle the melted 1 stick of butter over the dough and smear it all over the surface with your fingers. Mix together 1/2 cup sugar, 1/2 cup brown sugar, and the cinnamon, nutmeg, and ginger. Sprinkle this all over the surface of the dough, covering all the melted butter. Starting at the top, use a "typewriter" motion to roll the dough toward you into a large log. Roll it tightly as you go so the rolls with be nice and neat. When it\'s all rolled, pinch the seam closed and turn the roll over so that the seam is facing down.
Slice 1/2 to 3/4 inch slices and place them in the greased pan(s). Allow them to rise for 20 minutes, then bake for 15-18 minutes or until nice and golden brown around the edges.
For the Frosting- While the rolls are baking, making the frosting by combining all the frosting ingredients in the bowl of an electric mixer. Beat until fluffy, adding more milk if you\'d like a thinner icing. Add maple flavoring if using and beat until combined.
When the rolls come out of the oven, frost the immediately then let cool for 10 to 15 minutes before serving. This allows the frosting to get inside all the crevices and cracks between the rolls! Serve warm and enjoy!