Reduce the heat to low, stir in the flour, and cook for 2 minutes. Add the light brown sugar, vinegar, and a pinch of salt and cook until onions are deeply golden and very soft, an additional 15 mins.
Add the wine, bring to a boil, and then reduce to a simmer. Be sure to scrape up all the brown bits from the bottom of the pot as you deglaze with the wine.