Our friend Sara Hotchkiss gave us a link to this recipe. They are amazingly good, and if you can refrain from eating them immediately, they freeze great to go on pizza, sandwiches, crackers, and more, all winter long. The website for Gardener’s Supply with a slideshow of how to make them is here.
This recipe is for a 7-quart pot of onions, so reduce the oil, sugar, and vinegar accordingly for the quantity you have. A heavy pot (like cast iron) is ideal, so they can simmer slowly for two hours without worry of scorching.
Peel onions, then slice thinly. Put a half cup of olive oil in the bottom of the pot and start with a medium-low flame. You don’t want to fry the onions. They should not get brown and crisp. The goal is to cook them gently. Use a wooden spoon to gently mix them around, separating the rings and getting them all coated with a little olive oil. The onions should first become white and soft, not browned. Once they are almost completely covered in their own juices, keep them simmering. Once all of the onions have full softened and some of the moisture has evaporated, add 1/2 cup of brown sugar and 1/4 cup of the best balsamic vinegar you can afford (for a 7-quart pot initially filled to the brim with onions). Stir well and keep simmering. Once everything is caramel-colored and slightly thickened, they are ready. Cook much more than this phase and they start getting dried out.