Pumpkin Cinnamon Rolls with Maple Icing

0 Preheat oven to 400 F / 200 C.
1 Rub the bottom of a 9"x9" baking dish with 4 Tablespoons softened butter.
2 In the bowl of a stand mixer fitted with the dough hook, combine warm water, yeast, and sugar. Let stand until creamy, about 5 minutes.
3 Meanwhile, dust a kitchen counter lightly with flour.
4 To the yeast mixture, add 2 Tablespoons butter, salt, pumpkin pie spice, and 2 cups of flour. Mix on low until the ingredients come together.
5 Continuing to mix on low, add 1 more cup of flour and mix for 1 minute. Add the remaining 1 cup flour. Mix on low until all the flour is mixed in. Increase mixer speed to medium. Mix for 5 minutes, until the dough is smooth and elastic and begins to make a slapping sound as it hits the sides of the bowl.
6 Remove the bowl from the mixer and let the dough rest in the bowl (preferably near the warm oven), until the surface is smooth, about 5 minutes.
7 While dough rests, make filling by combining pumpkin, brown sugar, and cinnamon.
8 Turn the dough out on a floured surface and roll it a 9"x18" rectangle with a long side facing you. (Note: Don't worry about being precise; use the base of your 9"x9" baking dish as a general guide.) Use your hands to rub 4 Tablespoons of butter over the surface of the dough.
9 Spread pumpkin filling over the surface of the dough. .
10 Starting with the side closest to you, roll the dough into a tube. Use a serrated knife to cut 9 even slices. Place the slices in the prepared baking dish and let rise in a warm place (preferably near the warm oven) until the edges of the rolls are touching, 20 minutes.
11 Bake until golden brown on top, 20-25 minutes.
12 While the rolls are baking, use a hand mixer to beat 3 Tablespoons of butter and cream cheese until light and fluffy. Add powdered sugar, vanilla, and 3 Tablespoons milk. Continue mixing until icing is smooth. Add more milk a bit at a time, if needed, until icing is shiny and easy to pour.
13 When the rolls come out of the oven, let them cool for 5 minutes before topping with the icing.
14 Serve immediately (of course...who could wait!).