In the bowl of a stand mixer or in a large bowl, stir the yeast in warm water and let sit for 2 minutes.
Add 3 2/3 cups of flour, pumpkin puree, milk, 5 Tbsp melted butter, 2 Tbsp granulated sugar, 1 tsp pumpkin pie spice, and salt. Beat with a mixer at medium speed (or use a hand mixer) until smooth.
Using the dough hook on your mixer, knead dough for about 6 minutes, adding the remaining cup of flour little by little throughout the kneading process. If you don't have a mixer or a dough hook, you can knead dough by hand on a well floured surface. You should knead for about 10 minutes.
Place the dough in a large bowl that has been lightly coated in vegetable oil. Make sure the dough is lightly coated in the oil, cover the bowl with a kitchen towel, and let it rise for about an hour in a warm spot (if your kitchen is cool, you can turn your oven on low and set the bowl on top).
Once dough has risen, punch it down and let rest for about 5 more minutes.
Place dough on a well-floured surface and, using a rolling pen, roll dough into a large rectangle, about 30×10 inches (if you don't have a big enough surface, you can split the dough into two portions and make two separate rolls).
In a medium bowl, mix together remaining 1/2 cup granulated sugar, brown sugar, remaining 2 tsp pumpkin pie spice, and cinnamon together.
Pour about 10 Tbsp of the butter over the surface of the dough (save the rest for the pans) and use a pastry brush or your fingers to spread the it evenly.
Generously sprinkle the sugar/spice mixture over the butter.
Starting at the long end farthest from you, roll the dough tightly toward you. Use both hands and work slowly. Pinch the seams together.
Transfer the dough to a cutting board and, using a sharp knife, slice 1-inch slices. Lightly brush remaining melted butter into pie pans or baking dishes. Place the rolls in the pan, taking care not to overcrowd them (8-9 should fit in each pan).
Pre-heat oven to 375 degrees (If you’re using glass pans for your cinnamon rolls, pre-heat to 360 degrees instead). Cover the rolls with a kitchen towel for about 20 minutes, so they can rise again. Then bake for 17-20 minutes, until the cinnamon rolls are just turning golden.
Pour the icing over the cinnamon rolls while they're still warm.