Melt the butter in a small saucepan over medium heat. Add the milk and stir. Warm the mixture just until it reaches between 110-115 degrees F.If it gets too hot, let it sit for a few minutes until it cools down to the correct temperature. It's important that you check the temperature - if it's too cold, it won't activate the yeast, and if it's too hot, it will kill the yeast.

Remove the saucepan from the heat. Stir in the yeast and 1 teaspoon of the sugar. Let stand for 5 to 10 minutes until it begins to foam and bubble; this will let you know that the yeast is active.Baker's Note: If using instant/rapid rise yeast, you can choose to skip this step of proofing the yeast in the warm liquid first, and simply add the warm liquid and the yeast to the rest of the dough ingredients. However, I like to proof the yeast every time, simply to ensure the yeast is active and not expired, before adding it to the dough.

In the bowl of your stand mixer, stir together the flour, the remainder of the sugar, salt and spices. Add the warm milk mixture, egg, pumpkin and vanilla, and stir into a shaggy dough.With the dough hook, knead on medium/low speed for 10 minutes. The dough will be soft, sticky and loose, but don't add more flour.

Lightly spray a large bowl with nonstick baking spray. Place the dough in the bowl, cover tightly with plastic wrap, and set in a warm place to rise until doubled in size, about 45-90 minutes.If your oven has a bread-proofing setting, you can use that to proof your dough. If not, let your oven preheat to the lowest setting, turn the oven off, and then set your dough inside to rise.

Set the bowl of dough, still covered, in the refrigerator to chill for at least 2 hours, or overnight.The chill time allows the gluten to rest and the dough to develop flavor. It's also much easier to work with the dough when it's cold, since this is a soft dough.

Butter a 9x13 baking dish.

Turn the cold dough out onto a lightly floured work surface. Roll your dough out into a rectangle measuring approximately 12x18 inches.

Melt the butter and use a pastry brush to spread it evenly over the dough, all the way to the edges.In a small bowl, mix together the brown sugar and cinnamon, then sprinkle that evenly over the butter.

Roll up the dough (starting on one of the long sides) into a log, keeping it as tight as you can. Using a gentle sawing motion with a sharp, non-serrated knife, cut the dough into 12 rolls. You can also use unflavored dental floss to cut the dough, by sliding the floss under the log of dough, then crossing it over the top to cut through.

Place the rolls, cut side up, in the pan. Cover the pan with a towel, and set in a warm place for 20-30 minutes to puff up a little, just until the rolls are touching.

Preheat the oven to 350 F.

Bake the rolls on the center oven rack for about 25-30 minutes, until they're golden brown, and a digital instant read thermometer inserted in the center of the rolls reads 185 F.

In a bowl, use an electric mixer to beat the butter and cream cheese until smooth. Add the remaining ingredients, and beat until smooth and fluffy.

Let the rolls cool for about 10-15 minutes, then swirl the icing on top of the rolls.