In a small saucepan, heat the milk and butter just until warm (120 - 130°) and butter is almost melted, stirring constantly.
In large bowl, combine the pumpkin, sugar and salt. Add the warm milk mixture and beat with an electric mixer until well mixed. Beat in the egg and yeast. In a separate mixing bowl, whisk together the two flours. Add half of the flour mixture to the pumpkin mixture. Beat mixture on low speed for 5 minutes, scraping sides of bowl frequently. Add the remaining flour and mix thoroughly (dough will be very soft). Transfer the dough to a lightly greased bowl, then grease the surface of the dough lightly. Cover and let rise in a warm place until doubled, about 1 hour.
Punch the dough down. Turn the dough onto a floured surface. Knead a few turns to form a smooth dough, sprinkling with enough additional flour to make the dough easy to handle. On a lightly floured surface, roll the dough into a 12x10-inch rectangle.
PREPARE THE FILLING:
In a small bowl, combine the brown sugar and cinnamon. Brush the surface of dough with the melted butter. Sprinkle with the brown sugar mixture. Beginning with the long side of the dough, roll up jelly-roll style. Pinch the seam to seal. With a sharp serrated knife, gently cut the roll into twelve 1-inch slices. Place the rolls cut-side-up in greased 9-inch-square baking pan. Cover and let rise until nearly doubled, 30 to 45 minutes.
BAKE THE ROLLS:
Preheat the oven to 350°F. Bake the rolls about 20 minutes, or until golden. Remove from the pan to a waxed paper-lined wire rack. Cool 10 to 15 minutes.
ADD THE ICING:
While the rolls are cooling, prepare the icing: In a small saucepan, heat the butter until melted. Stir in the brown sugar and milk. Stir in brown sugar and milk. Cool over medium-low heat for 1 minute. Transfer to a small mixing bowl and cool the mixture slightly. Stir in the vanilla, salt and powdered sugar (start with 1/2 cup). Beat with an electric mixer until well blended. If necessary, add more powdered sugar for desired consistency. Drizzle icing over warm rolls.
*If you'd like to begin preparing these the night before... Follow directions through putting the rolls in the pan, then cover and refrigerate overnight. Take them out in the morning and let them rise for 45 minutes (maybe a bit more because the dough will be cold). *If you're lacking a warm place for rising, use your oven. Turn on the oven light. Then set your oven to 400 degrees for one minute. Turn it OFF and then place your pan inside the warmed oven. Make sure you have turned off your oven!