Peel and slice onions in half. Cut into thin slices.
Heat oil in a large skillet over medium heat. Add onions and cook, stirring occasionally, until soft, 8 to 10 minutes.
Add brown sugar, thyme, bay leaf, salt, wine, and balsamic vinegar. Reduce heat to very low and simmer, slightly covered, until liquid is reduced and almost gone, 1 to 1 1/2 hours.