To Make the Dough:

1. In a small bowl, dissolve the yeast in the warm water. Let stand for 5 minutes, until the yeast is activated and the mixture is a little foamy. Set aside.
2. In a large bowl, mix together the flour, pumpkin puree, milk, melted butter, sugar, pumpkin pie spice, and salt. Mix in the yeast mixture until a thick dough forms. Turn dough out onto a floured surface.
3. Begin kneading, adding a little flour at a time, until the dough is soft and elastic and no longer sticky.
4. Place the dough in a large bowl that has been lightly oiled, turning to coat the entire surface. Cover and let rise in a warm, draft-free place for 45 minutes, or until doubled in size.

To Make the Filling and Assemble:

1. While the dough is rising, prepare the cinnamon filling. Mix the softened butter, brown sugar, vanilla extract, and cinnamon in a small bowl until smooth. Set aside.
2. Punch the dough down. Cover and let rest for 5 minutes. Lightly flour a clean work surface. Roll the dough into a large, 12-by-10-inch rectangle on a floured surface. Spread the cinnamon mixture in an even layer over the dough, leaving a bit of a border at the edges.
3. Roll up the rectangle tightly, starting with the long edge, pressing firmly to get rid of any air pockets. Pinch the seam and ends to seal. Roll over so the seam is on the bottom. Cut into 8 thick slices. For smaller pieces, cut into 12 even slices. Place slices in a lightly buttered square pan. If making more rolls, use a 9×13-inch rectangular pan. Cover with a clean towel and let rise for another 45 minutes, or until doubled in size.
4. Preheat the oven to 375°F. Remove the towel from the pan, and bake the rolls for 20 minutes, or until golden brown. Remove and let cool slightly.

To Glaze and Serve:

1. After the cinnamon rolls have cooled for about 10 minutes, spread the frosting evenly over the top. Serve while still warm.