My own recipe. I made these for a neighborhood Thanksgiving dinner in 1996. I remember because it was the weekend that I learned I was pregnant with Eden.
Nonstick vegetable oil spray
3 medium onions (about 2 ½ lbs.) peeled, each cut vertically through root end into 12 to 14 wedges
4 tablespoons butter
1 cups canned chicken broth
1 ½ tablespoons sugar
1 tablespoons red wine vinegar
1 1/2 pounds slender green beans, ends trimmed
Preheat oven to 450 degrees. Line a baking sheet with foil and spray with vegetable oil spray. Arrange onions in a single layer on prepared sheet.
Dot onions with 2 tablespoons butter, dividing equally. Season with salt & pepper. Bake until onions are dark brown on bottom, about 35 minutes.
Meanwhile, boil broth in a large skillet over high heat until reduced to 1/4 cup, about 6 minutes. Add sugar and vinegar and whisk until sugar dissolves and mixture comes to boil.
Add onions to sauce; reduce heat to medium-low. Simmer until liquid is slightly reduced, about 5 minutes. Season with salt and pepper. (Can be prepared a day ahead, cover and refrigerate.)
Cook green beans in a large pot of boiling salted water until crisp-tender, about 5 minutes. Drain well. Return beans to same pot. Add remaining butter and toss to coat. Mound beans in large shallow bowl. Top with onion mixture and serve.