First we will begin making the dough. Heat up milk in a small sauce pan until it begins to simmer. Remove from heat and add salt and stir. Let it cool down to lukewarm to the touch. While milk is cooling, proof the yeast by adding the warm water, sugar, and yeast in a small bowl and stirring together. Let it activate by setting it aside for 10 minutes.
Once milk is cool, add to a large bowl, along with 3 ½ cups of flour, 2 tablespoons of oil, eggs, pumpkin puree, spices, and yeast mixture. Stir together with a wooden spoon until combined. The dough will be very thick.
Place dough on clean counter surface and begin kneading the dough for about 5 minutes until the dough is smooth and elastic. If it starts to stick to the counter, add a little flour. Once you finish kneading, shape into a ball. Lightly grease another large bowl and place the ball of dough into bowl. Cover with a kitchen towel and let it rise for 1 ½ hours, where it will be double the size. I like to place mine in the microwave to keep it away from any cool draft from the A/C.
When dough has finished rising, remove cover and, using your fist, punch the dough down and remove from the bowl. Roll out on a well-floured surface into a 18x24 inch rectangle and spread 3 tablespoons of softened butter to the edges. Mix the brown sugar with the remaining cinnamon and nutmeg and sprinkle evenly across the butter.
Roll the dough into a log, starting from one end to the other, lengthwise, so the log is 24 inches. Using a serrated knife, gently cut 15 slices with a sawing motion (try not to push too hard to pinch the dough), this will give you 15 cinnamon rolls. Quick tip: to make sure the slices are even, cut the log in three even sections, then cut each section into 5 even slices.
Grease a 9x13 baking pan. Add the cinnamon rolls to the greased pan in three rows of five. The cinnamon rolls will be slightly touching. Cover with a towel and let them rise for another 30 minutes. Preheat oven to 375 degrees.
Once the cinnamon rolls have risen, bake in the preheated oven for 25 minutes or until the tops have turned golden brown. Remove from oven and let them cool while you make the icing.