In a small bowl, dissolve yeast in warm water and set aside.
In a stand mixer bowl, combine milk, sugar, melted butter, pumpkin puree, spices, salt, and egg with a spoon. Attach the bowl to the mixer with the dough hook attached. Add 2 cups of flour and mix until smooth. Add yeast mixture. Mix in remaining flour until dough is easy to handle. Knead with dough hook for about 5 minutes. (If not using a stand mixer, knead dough on lightly floured surface for 5 to 10 minutes.) Place in well-greased bowl, cover, and let rise until doubled in size, usually 1 to 1 1/2 hours.
When doubled in size, punch down dough. Roll out on floured surface into a 15 by 9-inch rectangle. Spread softened butter all over dough. In a small bowl, mix together sugar, cinnamon, and pumpkin pie spice. Then sprinkle over buttered dough. Beginning at the 15-inch side, role up dough and pinch edge together to seal. Cut into 12 to 15 slices.
Coat the bottom of 13 x 9 baking pan with butter and sprinkle with sugar. Place cinnamon roll slices close together in the pan and let rise until dough is doubled, about 45 minutes. Preheat oven to 350 degrees F.
Bake for about 30 minutes or until nicely browned.
Meanwhile, mix cream cheese, butter, powdered sugar, salt, maple extract, and vanilla extract until smooth. For a thicker icing, add more powdered sugar. Spread over slightly cooled rolls.