Combine warm milk and yeast in a bowl until the mixture becomes foamy.
Mix flour, sugar, salt, and pumpkin puree in a large stand mixer until combined.
Add the yeast mixture to the flour bowl and knead until the dough is smooth and elastic.
Cover the bowl with a clean towel and let it rise in a warm spot for one hour.
Roll the proofed dough out into a large rectangle on a floured surface.
Spread softened butter evenly across the dough surface leaving a small margin at the edges.
Sprinkle a mixture of brown sugar and pumpkin spice over the buttered surface.
Roll the rectangle tightly into a log and cut into twelve equal pieces using a sharp knife.
Place the rolls into a greased baking dish and allow them to rise again.
Bake at 375 degrees Fahrenheit for 25 minutes until golden brown.
Beat the cream cheese until smooth and spread over the warm rolls before serving.