Step 1: Mix the ingredients. Put the yeast in warm milk and let it dissolve. Grab a bowl and mix together the egg, butter, pumpkin, salt, sugar, and yeast/milk mixture, plus 1 cup of flour. Using an electric/stand mixer and mix for 3 minutes on medium. Stir in the rest of the flour to make a sticky dough. *If you do not have a stand-mixer, you can mix dough in a large mixing bowl with a wooden spoon or even using your hand.*
Step 2: Add dough to the bowl. Just add the sticky dough to the bowl and do not knead it at all. The bowl should be greased and turn the sticky dough once so that the top is greased. Cover the dough and put it in a warm place. Let it rise so it's double its size. This should take about 1-1.5 hours.
Step 3: Make the filling. To make the filling in the rolls, mix the cinnamon, pumpkin pie spice and the brown sugar. Stir the dough mixture, beating it down. Put it out on a floured surface and roll it into a 18×10 inch rectangle. Spread softened butter on top evenly and then sprinkle on the spices and brown sugar mixture. Roll the dough into a cylinder and pinch the seam to seal. Slice the dough into 10-11 pieces, using a very sharp knife.
Step 4: Bake. Arrange the pieces onto a greased 9-inch or 11 inch pan. Cover them and put them in a warm place. Let them rise until doubled which will take about 45 minutes of time. Preheat the oven to 350 degrees F. Bake for about 23-27 minutes and then place on a wire rack to cool.
Step 5: Top with the Icing. Make Icing by beating softened cream cheese for a minute. Add and beat in confectioners' sugar, milk, pumpkin pie spice and vanilla next, till the icing gets smooth and spread it over on slightly warm rolls.