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

Combine wet ingredients: Add the egg, melted butter, pumpkin pie spice, cinnamon, and salt to the yeast mixture. Whisk until well combined.

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

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

Prepare filling: While the dough is rising, mix together the softened butter, brown sugar, cinnamon, and pumpkin puree.

Assemble rolls: Punch down the dough and roll it out into a large rectangle. Spread the filling evenly over the dough. Roll up the dough tightly, starting from a long side.

Cut and bake: Cut the roll into 12 equal slices and place them in a greased 9x13 inch baking pan. Cover and let rise for another 30 minutes.

Bake: Bake at 375°F (190°C) for 25-30 minutes, or until golden brown. Let cool slightly before frosting.

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

Frost and serve: Frost the warm cinnamon rolls and serve immediately.