The Pinkie (2014) on Netflix

Plot summary

Ryosuke cannot shake off Momoko, who has trailed after him since the two of them were five years old. Her devotion is so complete that she has surgeons reshape her face to match the looks he prefers, but he still avoids her and chases short-lived romances instead. One of those romances is with the girlfriend of a gangster boss, and when the boss finds out, he has Ryosuke's little finger chopped off. The severed finger ends up in Momoko's hands, and from it she grows a copy of Ryosuke, giving her the man she has always wanted, or a version of him.