In a large pot, cook EVOO and onions over medium-high heat, stirring occasionally, until softened, about 12 minutes. Add brown sugar and nutmeg; reduce heat to medium- low and cook, stirring often, until onions are golden and very soft, 30 to 45 minutes. Add wine; scrape up browned bits and cook until the wine is reduced by half, about 3 minutes. Add broth, bring to a boil and then simmer until liquid is slightly reduced, about 15 minutes; season with salt and pepper. Serve immediately or use as a base for the variations.