Mix together your fed sourdough starter, water, flour, oil, and honey in a large glass bowl. Form into a ball. Lightly grease the bowl and leave covered for 12 to 24 hours so the dough can rest.
Add the egg, baking powder, baking soda, and salt to the dough, and mix together with a dough hook or your hands. The dough should not be overly sticky but should form together enough to be rolled out. If it’s too wet, add a tablespoon of flour at a time and mix together until the dough is not sticky but not crumbly. If it’s too dry, add a teaspoon of water to the dough until it is not crumbly and forms together as a ball.
Roll the dough out on a lightly floured surface, to about 1/4 of an inch thick rectangle.
In a separate bowl, mix together the softened butter, cinnamon, and white sugar. Using a kitchen brush or your hands, spread this mixture over the top of your rolled out dough.
Tightly roll the dough up and cut the roll into 12 even roll sections. Place these rolls onto a well-seasoned 12-inch cast iron skillet.
Pour the 1/2 cup heavy whipping cream into the skillet and allow the rolls to soak in the cream and rise for 30 to 60 minutes in a warm place.*
Bake the rolls at 375F for 15 to 20 minutes until the tops of the rolls are golden brown.
While the rolls are baking, combine the cream cheese, butter, milk, powdered sugar, and vanilla together to make the cream cheese frosting.
When the rolls are done, allow them to slightly—but not completely—cool, and frost them with the cream cheese frosting.