Warm the milk and butter together over the stove or in the microwave until the butter is just melted. Set aside.
Whisk the pumpkin puree, sugar, nutmeg, and salt together in a large bowl or in the bowl of your stand mixer. Whisk in the warmed milk/butter, egg, and yeast until combined.
Using the dough hook or paddle attachment on low speed or mixing by hand, mix in 1 cup of flour. Mix for 1 minute, scraping down the sides of the bowl as needed. Add 1 and ⅔ cups more flour and beat for 1 more minute.
Knead the dough for 5 full minutes, or until it feels soft and slightly tacky. Let it rise in a greased bowl for 2 hours or until double in size.
Punch down the dough and roll it into a 10x14-inch rectangle. Spread softened butter on top, then sprinkle with the brown sugar, cinnamon, and spices mixture. Roll it up tightly and cut into 10-12 rolls.
Place the rolls in a greased baking dish and let them rise until doubled in size, about 1 hour.
Preheat oven to 350°F (177°C) and bake rolls for about 22-28 minutes or until lightly browned.
Make the icing by beating the cream cheese until smooth, then adding maple syrup, milk, and confectioners’ sugar. Spread on warm cinnamon rolls.
