Set aside 1/2 cup of flour.
In the bowl of your stand mixer add 2 1/4 cups of flour, sugar, salt, and yeast together until evenly mixed with a rubber spatula and then set on the mixer stand.
In a double boiler (not sure how to make a double boiler, learn how to make a double boiler at home) combine the water, milk, and butter together until the butter is melted and the mixture is hot to touch. You can also do this step in the microwave if preferred.
Add the dough hook to the mixer.
Pour the butter mixture into the flour mixture and mix on low speed until combined.
Next add the egg and the leftover flour to the cinnamon roll dough mixture, to make a soft dough. Start with 1/3 a cup working up to using 1/2 cup until the dough is ready. Keep the mixer on low speed while adding the flour and then up to medium speed to finish making the dough.
The dough is ready when it pulls away from the side of the bowl and has an elastic consistency.
Remove the dough from the stand mixer and Knead the dough for about 3-4 minutes on a floured surface.
Grease the stand mixer bowl, and add the dough back into the bowl and cover with a kitchen towel. Leave the dough in the bowl to rise and rest for about 10 minutes.
While the dough is rising make the cinnamon rolls filling.
Once your dough is ready, roll it out in a rectangle. Spread the pumpkin cinnamon roll filling on the dough.
Roll up the dough tightly by squeezing the edges closed, then cut into 1- 1 1/2 inch wide pieces.
Spray a circle baking pan with nonstick cooking spray.
Place cinnamon rolls into pan, you want the top to be the part where you can see the filling on the inside.
Place the baking pan covered in a dish towel in a nondrafty area, and let the dough rise until the cinnamon rolls have about doubled in size. This will take 60-90 minutes.
Once they have doubled in size, preheat the oven to 375 degrees and when the oven is ready place in the oven and bake for 25-30 minutes until they are lightly browned.
In a bowl, combine the vanilla extract, cream cheese and butter together and cream together. Once creamed, add in the powdered sugar and mix well. You can also use a stand mixer for this.
Once rolls have been removed from the oven, frost using half the amount made. let them cool and then frost again.