In a large mixing bowl, combine 2 cups of flour, yeast, and granulated sugar.
In a saucepan, heat the pumpkin puree, melted butter, and milk until just warm.
Add the warm pumpkin mixture to the flour mixture and mix well.
Add the egg and salt; mix until combined.
Gradually add the remaining flour to form a soft dough.
Knead the dough on a floured surface until smooth and elastic, about 6-8 minutes.
Place the dough in a greased bowl, cover, and let rise in a warm place until doubled, about 1 hour.
Deflate the dough and roll it out into a rectangle on a floured surface.
Spread the softened butter over the dough, and sprinkle the brown sugar and cinnamon evenly over the top.
Roll the dough up tightly from one long side, then cut into 12 equal pieces.
Place the rolls in a greased baking dish, cover, and let rise again until nearly doubled, about 30 minutes.
Preheat the oven to 350°F (175°C).
Bake the rolls for 25 minutes or until golden brown.
In a small bowl, mix the cream cheese, powdered sugar, and vanilla extract until smooth.
Spread the icing over the warm cinnamon rolls before serving.