In the bowl of a stand mixer, combine milk, melted butter, pumpkin puree, egg, brown sugar, and salt. Whisk until combined.
Add in the instant yeast and flour. Use the dough hook and mix on low speed for 1 minute. If you see flour on the sides, stop and scrape it down with a spatula. Then mix on medium speed for 3 more minutes. If you don't have a stand mixer, you can knead the dough by hand for about 5 minutes.
First Rise: Grease a bowl with oil (vegetable, avocado, or canola oil works). Put the dough in the bowl and cover it with a towel or plastic wrap. Let it sit at room temperature for 1 hour or until it doubles in size.
Make the Filling: In a small bowl, combine brown sugar with cinnamon, nutmeg, and cloves. Set aside. Also, grease a 9x13-inch pan with some of the softened butter (or line it with parchment paper).
Shape the Rolls: On a lightly floured surface, roll out the dough into a 14x16 inch rectangle (35x45 cm). Spread the softened butter all over the dough, but leave a small ¼ inch border on the far (and short) sides. Sprinkle your sugar and spice mix over the butter and press it down lightly with your hands.
Roll up the dough starting from the 14-inch side. Make sure the roll is tight and the seam is at the bottom. Cut off about an inch from both ends and throw them away. Now cut the roll into 12 equal 1-inch pieces.
Second Rise: Place the cinnamon rolls into the prepared pan, cover with a towel (or plastic wrap) and allow to rise at room temperature for 45 minutes to 1 hour
Preheat the oven to 350°F (180°C) or 160°C if using a fan oven, then bake the cinnamon rolls for 20 minutes or until lightly golden. You don’t want to overbake these, as they can become tough and dry. Remove from the oven, and allow to cool for 10 minutes before applying the icing.
To make the icing, in a bowl, combine cream cheese with 1 tablespoon of maple syrup (or honey, or milk) and beat with a hand mixer until smooth. Add the powdered sugar, and slowly beat again until combined, then increase the speed and beat until smooth. Spread the icing on the cinnamon rolls and serve.