Directions

1. 1. Preheat oven to 450 degrees F. Spray two heavy large baking sheets with vegetable oil spray.
2. 2. Cut the onions vertically through root end into 12 to 14 wedges and arrange them in a single layer on prepared sheets.
3. 3. Dot onions with four tablespoons of butter, dividing equally. Season with salt and pepper. Bake the onions until they are dark brown on bottom, about 35 minutes.
4. 4. Meanwhile, boil the broth in a heavy large skillet over high heat until reduced to 1/2 cup, about six minutes. Add sugar and vinegar; whisk until sugar dissolves and mixture comes to boil.
5. 5. Add the onions to the sauce; reduce heat to medium low. Simmer until liquid is slightly reduced, about five minutes. Remove from heat and season with salt and pepper; reserve.
6. 6. Cook green beans in large pot of boiling salted water until crisp tender, about five minutes. Drain well, return beans to same pot and add remaining two tablespoons of butter; toss to coat.
7. 7. Mound beans in a large shallow bowl; top with onion mixture and serve.