Add the warm water, the yeast and the 2 tbsp sugar to the bowl of your stand mixer fitted with the dough hook attachment. Stir the mixture gently with a fork just until all the yeast is moistened and then set the yeast mixture aside for 3-5 minutes.
Into a separate bowl, measure the flour, sea salt, cinnamon and nutmeg and mix them together with a wire whisk until they're combined.
Once you've noticed the yeast has begun to grow, add the pumpkin puree, the egg, the 1/4 cup sugar, and the melted butter to the yeast mixture. Dump the dry ingredients into the bowl of the mixer as well, right over top of the wet ingredients. Turn the mixer on low and let the dough hook go to work combining the ingredients and forming a soft, sticky dough. Once the dough begins to form increase the speed just slightly and let the machine knead the dough for about 5 minutes. It's a good idea to keep an extra 1/4 cup of flour on hand, just in case your dough is a little too sticky and you need to add a little here or there to keep the dough together.
Remove the dough hook and form the dough into a ball with your hands, returning it to the bowl of the stand mixer and covering the bowl with plastic wrap. Place the dough in a warm, dry place in your kitchen and let the dough rise for 90 minutes or until it has more than doubled in bulk.
Roll the dough out on a floured surface into a large square, about 18 inches by 18 inches.
Combine the filling ingredients (sugar and spices) in a small bowl and spread the filling evenly over the surface of the dough. Starting with the end closest to you and rolling away from you, roll the dough up gently and as tightly as you can, creating a spiral pattern on the inside. Slice the log you've created into 8 rolls that are equal in size.
Grease a round cake pan with some butter.
Drizzle the maple syrup into the bottom of the greased pan and arrange the 8 rolls in the cake pan. Cover the pan loosely with plastic wrap to get the rolls ready for their last rise.
Now here's the best part about this recipe: you can easily turn it into an "overnight" recipe by completing all the steps up to this point in the evening and placing the rolls in the fridge to complete their last rise while you get your beauty sleep. The cool temperature of the fridge retards the yeast so it rises very slowly all night long. When you wake up in the morning, set your oven to 350 degrees Fahrenheit and place the rolls in the COLD oven (plastic wrap removed, of course). Because the rolls have been in the cold refrigerator all night they'll complete the last bit of their rise in the oven as the oven heats up. Once the oven reaches 350 degrees, set the timer for 25-30 minutes and the rolls will be perfectly done after that time.
Alternatively, if you'd rather get the whole recipe over with in one day, feel free to let the rolls rise at room temperature for another 30 minutes after you've placed them in the greased pan. Be sure to cover them with plastic wrap while they complete this last rise, and remove the plastic wrap before placing them in the oven that's been preheated to 350 degrees. The baking time is the same - 25-30 minutes at 350 degrees. The only difference is that you'll wait to put the rolls in the oven until the oven has reached the correct temperature rather than placing the rolls in the cold oven.
While you're waiting for the rolls to cool, add the softened cream cheese and the powdered sugar to a mixing bowl and cream them together with a rubber spatula. Once the mixture is creamy and smooth, add the milk a few teaspoons at a time until the glaze has reached a consistency that's somewhere between spreadable and drizzle-able (and now I'm making up words...). Once the rolls have cooled almost completely (it's okay if they're still a bit warm), pour the glaze over the top of the rolls and spread it around evenly with a rubber spatula. Drizzle the caramel sauce over the top and dig the heck in!!
These rolls keep in an airtight container at room temperature for up to 3 days. They freeze well without the glaze; simply thaw and reheat slightly before glazing.