Add flour and salt to a large mixing bowl.
Use a box grater to grate butter or use a fork to cut butter into pea-sized pieces in the flour mixture.
Add sourdough starter, pumpkin puree, water, and maple syrup. (do NOT add the egg or extra 1/2 cup of flour)
Mix until all ingredients are combined and a dough forms (may need to use your hands at the end).
Cover bowl with a damp dish towel or lid. Let dough ferment on the counter 8-10 hours.
When dough finishes fermenting, make the filling by stirring together cinnamon, cane sugar, and softened butter in a bowl until combined. Set aside.
Uncover dough and add egg plus the 1/2 cup of flour.
Use your hands to incorporate these ingredients. (This will be a little messy and takes a few minutes, but trust me it'll incorporate).
Once ingredients are incorporated, dust the counter with flour and roll the dough out with a rolling pin into a 12 inch by 6 inch rectangle. Dough should be about 1/2 inch thick.
Now spread filling in an even layer across rolled out dough. Make sure as much of the rectangle is covered as possible.
Roll the dough tightly into a log starting at the 6 inch side. When you get to the end, use your fingers to pinch the seam together down the log.
Using unflavored dental floss, a knife, or bench scraper cut the log into 8 rolls. Add each to a parchment lined baking sheet about 1/2 inch apart.
Cover baking sheet with a second piece of parchment paper, gently pressing the sides around the rolls.
Stick cookie sheet into the refrigerator for 2-12 hours.
Preheat oven to 400 degrees Fahrenheit.
After 2 hours minimum, take off top layer of parchment and bake for 25 minutes (use a knife to poke the centers after baking to ensure doneness).
While pumpkin cinnamon rolls are baking, make the frosting by adding all frosting ingredients together in a bowl and mixing with an electric mixer on low speed until fully combined 1-2 minutes.
Take rolls out of the oven and let cool on a cooling rack. Once cooled, add frosting and enjoy!