Add the warm water, yeast, and 2 tbsp sugar to the bowl of a stand mixer fitted with the dough hook attachment. Stir gently with a fork until the yeast is moistened. Set aside for 3-5 minutes.
In a separate bowl, whisk together the flour, sea salt, cinnamon, and nutmeg until combined.
Once the yeast starts to foam, add the pumpkin puree, egg, 1/4 cup sugar, and melted butter to the yeast mixture. Add the dry ingredients over the wet ingredients in the mixer bowl. Turn the mixer on low and use the dough hook to combine into a soft, sticky dough. Once it forms, increase the speed slightly and knead for about 5 minutes. Keep an extra 1/4 cup flour handy in case the dough is too sticky.
Remove the dough hook, form the dough into a ball, return it to the mixer bowl, and cover with plastic wrap. Place the dough in a warm, dry spot to rise for 90 minutes or until it has more than doubled in size.
Roll the dough out on a floured surface into an 18-inch square. Brush the surface with melted butter.
Mix the filling ingredients in a small bowl and spread evenly over the dough. Starting at the end closest to you, roll the dough tightly away from you to form a spiral. Cut the log into 8 equal rolls.
Grease a round springform pan with butter. Drizzle the maple syrup into the bottom of the pan and arrange the 8 rolls inside. Cover loosely with plastic wrap for the final rise.
For an overnight method, place the covered pan in the refrigerator to rise slowly overnight. In the morning, preheat the oven to 350°F and place the rolls (plastic wrap removed) in the cold oven. As the oven heats, the rolls will finish rising. Bake for 25-30 minutes once the oven reaches 350°F.
Alternatively, let the rolls rise at room temperature for an additional 30 minutes after placing them in the pan, covered with plastic wrap. Preheat the oven to 350°F, remove the plastic wrap, and bake the rolls for 25-30 minutes.
While the rolls cool, combine the softened cream cheese and powdered sugar in a mixing bowl. Mix until smooth, then gradually add the milk until the glaze reaches a consistency between spreadable and drizzle-able.
Once the rolls have cooled almost completely, spread the glaze evenly over the top with a spatula. Drizzle caramel sauce on top if desired and enjoy.