Add the dough ingredients into the bread machine in the order they are listed and set on the dough cycle.*
Once the dough cycle is complete, add the dough to a clean and floured countertop and turn the dough, kneading it until smooth. Divide into 2 balls and roll out into 2 rectangles.
Spread thin layer of butter, then pumpkin puree, then brown sugar and spice mix. Roll tightly and then slice into 1" inch wide rolls.
Place the rolls into greased baking dishes, leaving a little space between the rolls for them to expand and rise. Cover with dishtowel and let rise for an hour in a warm place in your kitchen.
Preheat oven to 350. After the rolls have risen, bake for 16-20 minutes, or until middle rolls are cooked through.
Prepare icing by mixing the powdered sugar with the spice mix, then gently stir in the pumpkin puree. Finally, add milk, 1/4 tsp at a time, mixing well until icing forms consistency you prefer.
Add icing to the tops of the rolls and serve warm.
*If you don't have a bread machine, you can make the bread by hand. In a small bowl, add the milk, sugar and yeast and let it proof. In a large mixing bowl, add the beaten egg and pumpkin puree, salt and then pour in the milk-yeast mixture and gently combine. Add the flour, one cup at a time, stirring into a wet dough, then into more of a dry dough. Cover with dishtowel and let rise in warm place. Once the dough is ready, complete directions listed above.