During Link's quest, he can meet an Old Man located one screen south of Gnarled Root Dungeon. He is found during the Summer when the water has receded, revealing a staircase. As soon as Link speaks with the Old Man, this triggers the side quest to acquiring the Red Ring. Four Golden Beasts will appear throughout the Overworld. One of these beasts is the Golden Darknut and it will appear one screen east of the entrance to the Hero's Cave.
The Golden Darknut is a significantly stronger version of a standard Darknut. Since it is only encountered during Spring, and the default season is Winter, Link will have to wait until he has access to the Tree Stump at the west portion of the Western Coast before he can encounter the Golden Darknut.