In a microwave safe bowl, or a small pot, heat milk and butter just until butter has melted and liquid is warm.
Place the milk and butter mixture in the bowl of a stand mixer with the dough hook attached. Add in the pumpkin. Mix just until blended.
Add the remaining ingredients and mix for 5-7 minutes until dough pulls away from the sides of the bowl and is smooth.
Place in a lightly oiled bowl, cover with plastic wrap, and let rise in a warm place for 45 minutes.
Turn dough out onto a lightly floured surface and roll out to approximately 18x12 inches.
Spread the softened butter over the dough, leaving 1 inch bare on the long side, then sprinkle with brown sugar and pumpkin pie spice. Lightly press the filling down with your hand, then roll the dough up from the long side, finishing on the side you left bare.
Pinch seam to seal. Using a sharp knife, slice into 12 equal sized rolls.
Place in a lightly greased 9x13 pan, cover with plastic wrap and allow to rise 45 minutes.
Preheat oven to 375°F and transfer rolls in the oven.
Bake for 25-30 minutes, until golden brown.
Remove from the oven, allow to cool for 10 minutes, then drizzle with icing.
FOR THE ICING
In a small bowl, mix the cream cheese, butter and vanilla until smooth.
Add the powdered sugar and 2 tablespoons of the milk and mix. Continue adding remaining milk until icing reaches your desired consistency.
Drizzle icing over the warm rolls and try not to eat 5 of them! So delish!