Heat oil in a large skillet over medium heat. Add onions and cook, stirring occasionally, until golden, 10 to 15 minutes.
Meanwhile, bring a large saucepan of lightly salted water to a boil. Add green beans and cook, uncovered, until crisp-tender, 6 to 7 minutes. Drain.
Add broth to the onions; cook for 5 minutes. Stir in vinegar, brown sugar, salt and pepper. Add the beans, cover and cook for 2 minutes. Serve warm.
Commercial vegetable broth is readily available in natural-foods stores and many supermarkets. We especially like the Imagine and Pacific brands, sold in convenient aseptic packages that allow you to use small amounts and keep the rest refrigerated.
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