In a large bowl, combine warm milk, yeast, and sugar. Let stand for 5-10 minutes until foamy. Whisk in the egg, salt, and melted butter.

Gradually add the flour, one cup at a time, mixing with a wooden spoon or spatula until a shaggy dough forms. Stir in the pumpkin puree.

Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, until smooth and elastic. Add a little more flour if the dough is too sticky.

Place the dough in a lightly oiled bowl, turning to coat. Cover with plastic wrap and let rise in a warm place for 1-1.5 hours, or until doubled in size.

While the dough is rising, combine the softened butter, brown sugar, cinnamon, and ginger (if using) in a medium bowl.

Punch down the dough and turn it out onto a lightly floured surface. Roll the dough into a 12x18 inch rectangle. Spread the cinnamon filling evenly over the dough. Tightly roll the dough up from the long side into a log. Cut the log into 12 equal slices.

Place the rolls in a greased 9x13 inch baking pan. Cover with plastic wrap and let rise for another 30-45 minutes, or until puffy.

Preheat oven to 350°F (175°C). Bake for 25-30 minutes, or until golden brown. While the rolls are baking, beat together the softened cream cheese and butter until smooth. Gradually add the powdered sugar, beating until combined. Stir in the vanilla extract and add milk, one tablespoon at a time, until desired consistency is reached.

Let the rolls cool slightly before frosting. Enjoy!