In a small bowl, combine the warm milk and yeast. Let sit for 5 to 10 minutes until foamy.

In a large mixing bowl, whisk together the pumpkin puree, granulated sugar, egg, melted butter, salt, and cinnamon. Stir in the yeast mixture.

Add the flour gradually, mixing until a soft dough forms. Knead on a lightly floured surface for 6 to 8 minutes, or until smooth and elastic, adding a little more flour only if needed.

Place the dough in a lightly greased bowl, cover, and let rise in a warm place for 1 to 1 1/2 hours, or until doubled in size.

While the dough rises, mix the brown sugar, granulated sugar, cinnamon, ginger, and nutmeg in a small bowl for the filling.

Punch down the dough and roll it out on a floured surface into a rectangle about 16 by 12 inches. Spread the softened butter evenly over the surface, then sprinkle the filling mixture over the top.

Starting from the long side, roll the dough into a tight log. Cut into 12 equal rolls and place them in a greased 9x13-inch baking dish.

Cover the rolls and let them rise again for 30 to 45 minutes, until puffy.

Preheat the oven to 350°F (175°C). Bake the rolls for 22 to 28 minutes, or until golden brown and cooked through.

While the rolls bake, make the frosting by beating together the cream cheese and butter until smooth. Add the powdered sugar, maple syrup, cooled coffee, vanilla, and salt, then beat until light and creamy.

Spread the frosting over the warm rolls and serve.