Combine milk and butter into a glass measuring cup, microwave for 45 seconds on high. Stir to melt the butter, continue heating until the mixture reaches 110°F.
In the bowl of a stand mixer, whisk together: flour, sugar, pumpkin pie spice, and salt.
Once the milk mixture is 110°F add the packet of active dry yeast and stir. Wait until the mixture is bubbling and add to the dry mixture from step 2.
Add pumpkin puree and egg, fold the mixture to gently combine before using the stand mixer.
Using the dough hook on your stand mixture, beat on medium-low speed for 5 minutes.
Place the dough into a greased bowl, cover with plastic wrap and refrigerate overnight.
The next morning, turn out the dough on a floured work surface. Using a rolling pin, roll out the dough into a large rectangle.
For the Filling: Mix in a small bowl: sugar, brown sugar, cinnamon, and pumpkin pie spice.
Spread softened butter on dough, sprinkle filling mixture on top of the butter. Make sure it’s evenly dispersed and pressed into the butter.
Starting from the largest side, roll the dough into a spiral. Using dental floss, cut the dough sections and place them into a greased Pyrex Deep Pie Dish.
Cover with a damp towel and let rise for 25 minutes.
Once risen, bake at 350°F for 15-20 minutes.
While baking, mix together frosting: cream cheese, butter, maple sugar, and vanilla. Once combined, add powdered sugar, mix until smooth.
When rolls are done baking, let cool slightly, then spread frosting over warm rolls.