In large skillet over medium-high heat, cook onions in olive oil, uncovered, stirring occasionally. The more caramelized brown you get them, the better the flavor will be. This will take 45-60 minutes.
I was in a hurry, so I didn't really get these onions caramelized, but it'll still be good. Stir in remaining ingredients.
Continue cooking, uncovered, stirring occasionally, for 35-45 minutes until the liquid reduces significantly and becomes a syrupy consistency.
Cool completely and store, covered, in refrigerator.
NOTE: I'm a balsamic vinegar junkie and buy the expensive premium balsamics at a specialty store. BUT, for onion jam I use regular, grocery store balsamic vinegar. I've also made this substituting red wine vinegar, and it's also very good.
