Activate yeast: In a large bowl, combine warm milk, yeast, and sugar. Let stand for 5-10 minutes until foamy.

Add wet ingredients: Add egg and melted butter to the yeast mixture. Whisk to combine.

Add dry ingredients: Gradually add flour, pumpkin pie spice, cinnamon, and salt, mixing until a dough forms. Turn out onto a lightly floured surface and knead for 5-7 minutes until smooth and elastic.

First rise: 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.

Prepare filling: In a bowl, cream together softened butter, brown sugar, cinnamon, and pumpkin puree.

Assemble rolls: Punch down dough and roll it out into a 12x18 inch rectangle. Spread filling evenly over the dough. Roll up tightly, starting from a long side. Cut into 12 equal slices.

Second rise: Place rolls in a greased 9x13 inch baking pan. Cover and let rise for 30 minutes.

Bake: Bake at 375°F (190°C) for 20-25 minutes, or until golden brown.

Make frosting: While rolls are baking, beat together cream cheese and butter until smooth. Gradually add powdered sugar and vanilla extract, mixing until smooth. Add milk, one tablespoon at a time, until desired consistency is reached.

Frost and serve: Let rolls cool slightly before frosting generously. Serve warm.