Comments: It may seem unnecessary to go through all this for just onions, but the end result is truly worth the time. The vinegar adds an acidic punch, the sugar makes these sweeter than they naturally would become, and the Vermouth adds complexity. I use this recipe to prepare a large batch that I then use in other dishes, such as Fritattas or savory Focaccia. Leftovers can be kept in a ziploc bag in the freezer for a couple of weeks, maybe longer, I just have never had them last any longer than that.
Ingredients (quantities are just guidelines here):
Onions-Usually 5-6 small yellow onions
¼ C Dry Vermouth
¼ C aged vinegar, such as balsamic, white balsamic, or sherry vinegar
¼ C brown sugar
1-2 T Vegetable Oil
Water-enough to cover onions in the pan
Salt and pepper to taste
Procedure: 
1. Slice, dice, French-cut, or chop onion any way you like to see them
2. Place in a large skillet with oil and over high heat and stir to coat onions
3. When onions just begin to sizzle, add all other ingredients and bring to a boil
4. Reduce heat and simmer for at least 30 minutes. Liquid should reduce slowly
5. When most of the water has boiled off and onions are in a syrup, increase heat to brown slightly, watching and stirring often to prevent from burning.