Can an ovarian cyst of this size (10 cm), eventually resolve itself?

EXTREMELY unlikely: I would almost say 100% no. That size of a cyst is too large to resolve itself, and should be removed surgically, due to the risks of it being a tumor (need to rule out malignancy) and due to the risk of torsion (where the ovary twists around it's artery and vein, cuts off the blood supply to it and causes severe pain). Sorry, but you really need to have surgery to remove it.