Place the unpeeled onions in a small saucepan. Add enough water to cover by 1 inch and bring to a boil over high. Boil until the onions are tender when pierced with a knife, 7 to 10 minutes. Drain; let cool. Peel and trim the onions, keeping the root end intact.
In a large skillet, heat the EVOO over medium, add the onions and cook, stirring occasionally, until onions begin to brown and sizzle, about 3 minutes. Add the vinegar and simmer, stirring often, until the onions are glazed, about 2 minutes. Season with sea salt. Serve warm or at room temperature.