In a large bowl, combine warm milk, yeast, and sugar. Let stand for 5 minutes until foamy.

Add egg, melted butter, pumpkin pie spice, cinnamon, and salt. Mix well.

Gradually add flour, mixing until a soft dough forms. Turn out onto a lightly floured surface and knead for 5-7 minutes until smooth and elastic.

Place dough in a greased bowl, turning to coat. Cover and let rise in a warm place for 1-1.5 hours, or until doubled in size.

While dough is rising, prepare the filling: In a bowl, cream together softened butter, brown sugar, cinnamon, and pumpkin puree.

Punch down the risen dough and roll it out into a 12x18 inch rectangle. Spread the filling evenly over the dough.

Tightly roll the dough into a log. Cut into 12 equal slices and place them in a greased 9x13 inch baking pan.

Cover and let rise for another 30 minutes. Bake at 375°F (190°C) for 20-25 minutes, or until golden brown.

Meanwhile, prepare the frosting: Beat together cream cheese and butter until smooth. Gradually add powdered sugar and vanilla extract, mixing until combined. Add milk, as needed, to reach desired consistency.

Let the rolls cool slightly before frosting generously.