For the dough—In a large bowl whisk together 3 cups flour, kosher salt, pumpkin spice, and nutmeg; set aside.
Gently warm the milk in a saucepan or the microwave to 100-110F°, or to your yeast manufacturer’s recommendation. Add the warmed milk, 1 tsp granulated sugar, and the yeast to a small bowl. Gently mix, and let stand until foamy, about 8-10 minutes.
While the yeast is proofing, in the bowl of a stand mixer fitted with the paddle attachment, mix together the melted butter, pumpkin puree, egg, brown sugar, and vanilla extract until smooth. Add the yeast mixture and mix on low to combine.
Stop the mixer and add the 3 cups of flour and mix on medium-low speed. Once it turns into a sticky dough, stop the mixer and switch to a dough hook. Continue mixing the dough on medium speed for about 5 minutes. Stop the mixer and check the dough. It should be soft and slightly sticky, but not so much that it sticks aggressively to your hands. If the dough seem too tacky, continue to add in the remaining flour in tablespoon increments. You may not need all the flour, so check the tackiness of the dough after each addition. The dough will be soft and should clear the sides of the bowl, but will still slightly stick to the bottom of the bowl
Place the dough into a lightly oiled bowl and cover with plastic wrap. You could use the same bowl you mixed it in, as it should be pretty clean. Place the dough in a warm, draft-free place. The oven or microwave are two great places. Let dough rise for 1-2 hours, or until doubled in size.
Place the dough onto a lightly floured surface and lightly punch down the dough. Cover and let rest for 10 minutes, then roll out into a 18x10-inch rectangle.
For the filling, mix together the brown sugar, cinnamon, and pumpkin spice. Spread the 4 tablespoons of softened butter over the surface of the dough, then sprinkle the filling evenly over the dough, leaving a ½ inch border on one side. With your rolling pin, lightly roll over the sugar mixture to help pack it into the dough.
Roll the dough lengthwise up from bottom to top, making sure to tuck and pull as you roll.
Run a moistened finger along the ½-inch edge of the dough without filling, and pinch to seal the edge. Cut into 12 pieces. They should be just over 1-inch thick. Place the rolls onto a 13" x 9" x 1"-inch baking sheet, cover with plastic wrap and let the dough rise for another 1-2 hours, or until doubled in size.
Depending on how quickly the rolls are rising, heat oven to 375 F°. Place the rolls in the oven and bake for 20-25 or until lightly brown on top. You don’t want to brown the rolls to much as this will make them harder when they cool.
While the rolls are baking, prepare the frosting.
In the bowl of a standing mixer fitted with a whisk attachment, mix together the cream cheese, vanilla, powdered sugar butter, and salt. Once combined, add in the butter and whisk until smooth.. Add a small amount of milk to create a more “glaze like” texture, continue to add milk until desired consistency is obtained.
Pour glaze over cinnamon warm buns and enjoy every bite!