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

Add the remaining sugar, pumpkin purée, egg, melted butter, salt, cinnamon, nutmeg, ginger, and cloves. Stir to combine.

Mix in 3 1/2 cups of the flour, then add more as needed until a soft, slightly tacky dough forms.

Turn the dough onto a lightly floured surface and knead for 6 to 8 minutes, until smooth and elastic.

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

Grease a 9x13-inch baking dish. Punch down the dough and roll it out into a rectangle about 16 by 12 inches.

Spread the softened butter over the dough. In a small bowl, mix the brown sugar, cinnamon, pumpkin pie spice, and pumpkin purée, then spread evenly over the buttered dough.

Roll the dough up tightly from the long side into a log and pinch the seam to seal. Cut into 12 even rolls.

Arrange the rolls in the prepared baking dish. Cover and let rise for 30 to 45 minutes, until puffy.

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

While the rolls bake, beat together the cream cheese and butter until smooth. Mix in the powdered sugar, milk or cream, vanilla, and salt until creamy and spreadable.

Let the rolls cool for 10 minutes, then spread or drizzle the frosting over the warm rolls and serve.