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. In a stainless steel skillet over medium heat, melt the butter. Swirl the pan occasionally to help the butter melt evenly. The butter will begin to foam, and then the foam will begin to subside and you’ll start to see tiny specks at the bottom of the pan, stir with a heat resistant spatula or wooden spoon and constantly stir and scrape so milk solids that are browning don’t stick. (These are what give brown butter it’s yummy flavor.) As soon as the butter turns chestnut brown and omits a nutty aroma, remove the pan from the heat and scrape the brown butter and all of the delish brown bits into a heat proof bowl. It’s important to remove to a bowl immediately so the residual heat from the pan doesn’t burn the butter. Place in the fridge so the butter can cool and 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