For the dough: In a large saucepan, combine the milk, vegetable oil and granulated 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 it to sit for 5 minutes. Stir in the pumpkin puree until combined.
Combine 4 cups of the flour with the cinnamon, ginger and nutmeg. 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 the baking powder, baking soda, salt and remaining 1/2 cup flour until totally combined.
Preheat the oven to 375 degrees F. Drizzle butter into 3 pie pans (or a larger baking dish) and smear it all over the bottom of the pans.
Turn out the dough onto a floured surface and press it into a rectangular shape. If it is overly sticky, sprinkle generously with flour until easier to handle. Flour a rolling pin and roll the dough into a large rectangle about 18 inches by 24 inches.
For the filling: Drizzle the melted butter over the dough and smear it all over the surface with your fingers. Mix together the brown sugar, granulated sugar, cinnamon, ginger and nutmeg in a medium bowl. Sprinkle this mixture all over the surface of the dough, covering all the melted butter. Sprinkle with 1/2 cup to 3/4 cup chopped pecans.
Starting at the top, roll the dough toward you into a large log, moving back and forth down the line of dough (in a "typewriter" motion) and always rolling toward you. 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 into 1/2- to 3/4-inch slices and place the slices in the buttered pan(s). Allow to rise for 20 minutes.
Bake until the rolls are nice and golden brown around the edges, 15 to 18 minutes.
For the frosting: While the rolls are baking, make the frosting by combining the cream cheese, powdered sugar, milk, butter and salt in the bowl of an electric mixer. Beat until fluffy, adding more milk if you'd like a thinner frosting.
Frost the rolls the second they come out of the oven. Sprinkle the extra pecans over the frosting, then allow them to sit for 15 minutes before serving.