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

Add the pumpkin puree, egg, melted butter, cinnamon, nutmeg, ginger, cloves, and allspice. Mix until combined.

Gradually add the flour and salt, stirring until a soft dough forms. Knead by hand or with a dough hook for 6 to 8 minutes, adding only enough flour to make the dough soft and slightly tacky.

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

While the dough rises, make the filling by mixing the softened butter, brown sugar, pumpkin puree, cinnamon, pumpkin pie spice, and salt until smooth.

Punch down the dough and roll it out on a lightly floured surface into a 16 by 12-inch rectangle.

Spread the filling evenly over the dough, leaving a small border around the edges.

Starting from the long side, roll the dough tightly into a log. Slice into 12 even rolls and place them in a greased 9 by 13-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 lightly golden and cooked through.

For the icing, beat the cream cheese and butter together until smooth. Add the powdered sugar, vanilla, salt, and 1 tablespoon of milk. Beat until creamy, adding more milk as needed for a spreadable consistency.

Spread the cream cheese icing over the warm rolls and serve.