Heat the oil in a large saucepan over medium-high heat. Add the onions, 1 teaspoon salt, and ½ teaspoon pepper. Cook, covered, stirring often, until soft, about 15 minutes. Uncover, reduce heat to medium, and cook, stirring occasionally, until the onions are a rich golden brown, 12 to 15 minutes.
Add the wine and cook, stirring occasionally, until it evaporates, 4 to 5 minutes. Stir in the vinegar and thyme. Serve warm or at room temperature.