To make pumpkin rolls, begin by preparing a cake pan. Mix together flour, sugars, yeast, salt, cinnamon, ginger, and cardamom in a stand mixer. Add butter, milk, egg, and pumpkin puree, mixing until the dough is soft and sticky. Let it rest for 30 minutes.
For the filling, combine sugars, spices, salt, and melted butter. Roll out the dough, brush it with butter, sprinkle the filling, then roll it into a log and slice into 10 rolls. Place them in the pan, let rise for 45 minutes, and bake at 350°F for 25-30 minutes.
Meanwhile, prepare the frosting by beating cream cheese, buttermilk, and confectioners' sugar until smooth. Pour the frosting over the baked rolls before serving.