In the bowl of a stand mixer, combine milk, yeast, and eggs. Add butter, pumpkin puree, brown sugar, and salt. Mix until smooth. Add flour a cup at a time until the dough isn't sticking to the bowl. You may not need to use all the flour. Place in a greased bowl and cover. Let it rise until doubled in size, about 1 hour.
Roll Out The Dough
Punch down the dough and place on a lightly floured surface. Roll into a large rectangle that is 24 inches long by 12 inches wide.
Make The Filling
In a small bowl, stir together softened butter, brown sugar, cinnamon, and pumpkin pie spice.
Fill, Roll, Slice
Spread the filling on the dough rectangle leaving about a ¼ inch around the edges.
Roll the dough along the long edge so you end up with a 24 inch long log.
Cut into 2 inch slices with a serrated knife. Place in a greased baking dish. Cover and let rise for 30 minutes.
Bake and Icing
Preheat oven to 350°F. Bake until golden brown and delicious, about 30 minutes.
Make the icing in a small bowl or measuring cup with pour spout. Combine powdered sugar, pumpkin pie spice, vanilla extract, and maple syrup. Add the milk a little at a time while stirring. You want a smooth icing that can be poured. Adjust with more milk if it is too thick or more powdered sugar if it is too thin.
Pour icing on hot pumpkin spice cinnamon rolls. Serve warm.
Notes
Expert Tip: Make them the night before. Follow all the above steps, but don't let them rise that second time. Cover with plastic wrap and refrigerate overnight. In the morning, let them rise for 30 minutes before baking.