In a large bowl, combine the warm milk, yeast, and 1 tablespoon of the granulated sugar. Let sit for 5 to 10 minutes until foamy.

Add the pumpkin puree, melted butter, egg, remaining granulated sugar, salt, cinnamon, nutmeg, ginger, and 2 cups of flour. Mix until smooth.

Gradually add the remaining flour, stirring until a soft dough forms. Knead on a lightly floured surface for 6 to 8 minutes until elastic and smooth, adding a little more flour if needed.

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.

Punch down the dough and roll it out into a rectangle about 16 x 12 inches.

Spread the softened butter evenly over the dough. In a small bowl, mix the brown sugar and cinnamon, then sprinkle it over the buttered surface.

Starting from the long side, roll the dough tightly into a log. Slice into 12 even rolls and place them in a greased 9 x 13-inch baking dish.

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

Preheat the oven to 350°F (175°C). Bake the rolls for 20 to 25 minutes, or until lightly golden and cooked through.

While the rolls bake, beat the cream cheese, powdered sugar, vanilla, and enough milk to make a smooth glaze.

Spread the glaze over the warm rolls before serving.