Heat the milk and butter in a small saucepan just until it reaches 105°F-115°F. It should be lukewarm so this won't take long at all. If milk gets too hot, it will kill the yeast and oh em gee we don't want that! Set milk/butter aside.
1/2 cup whole milk, 2 Tbsp. unsalted butter
In the bowl of a stand mixer with the whisk attachment on medium speed, combine the pumpkin, both sugars and salt. Add in the milk/butter mixture, egg and yeast just until combined. (We will use the heavy cream later)
1 cup 100% pumpkin puree, 1/4 cup sugar, 1/4 cup dark brown sugar, packed, 1 tsp. kosher salt, 1 large egg, room temperature, 1, .25 oz. package active dry yeast (2 1/4 tsp.)
Add the dough hook and add 1 cup of bread flour on medium speed. Mix for ~1 minute. Add another cup. Mix 1 minute, and repeat twice more. Scrape down sides to incorporate flour as needed. With the mixer on medium-low speed, knead the dough for ~8 minutes. Knead just until the dough is pulling away from the sides of your mixer, but is tacky (not sticky) to the touch.
4 cups bread flour, plus more as needed for surface and rolling
Grease a medium sized bowl with baking spray or oil and place the dough in the bowl, turn once to grease the top too. Cover with plastic wrap or a clean kitchen towel and allow to rise for 1 ½ hours - 2 hours. The dough should almost double in size.
During this time, make the brown butter for the cream cheese frosting. For a detailed tutorial, see this post on how to brown butter. Place the brown butter in the fridge so the butter can cool and solidify. This will take ~1-2 hours to solidify. 1/3 cup butter, unsalted
Grease a 9x13 inch pan with baking spray. You can line with parchment paper to catch any filling that may ooze out if desired.
Combine the ingredients together for the filling in a medium sized mixing bowl until smooth.
1/2 cup softened butter, unsalted, 2/3 cup dark brown sugar, packed, 1 Tbsp. ground cinnamon, 1 Tbsp. pumpkin pie spice
Roll out the dough. Turn out the dough onto a well floured work surface. Roll the dough into a large rectangle, spread the brown sugar filling all over the dough. Leave a small margin on the edges so you can roll, but I pretty much spread it all the way to the edge!
Roll the dough up tightly, slice with a sharp knife or use the floss method and arrange the rolls in the prepared pan. Cover tightly with plastic wrap and a warm kitchen towel and allow to rise again for 30 minutes - 1 hour. (Or see the overnight option in the notes below).
Preheat the oven to 350°F. Warm the heavy cream in the microwave for 15-20 seconds, just until lukewarm to the touch. Pour the cream over the cinnamon rolls right before you put in the oven. Bake for 20-22 minutes or until cinnamon rolls are lightly browned on top and reach an internal temperature of 190°F. Allow to cool for 5-10 minutes while you make the frosting.
1/2 cup heavy cream
Using a hand held mixer or the stand mixer, beat the prepared brown butter in a mixing bowl until smooth. Add the cream cheese and combine again until smooth. Add in the remaining ingredients and beat until creamy. Spread the frosting over warm rolls and enjoy!
8 oz. cream cheese, softened, 2 cups powdered sugar, 1 tsp. vanilla extract, 1/4 tsp. pumpkin pie spice, pinch of kosher salt