
Preheat oven to 450F. Spray 2 heavy large baking
sheets with
vegetable oil spray. Arrange onions in single layer
on prepared
sheets. Dot onions with 4 tablespoons butter, dividing
equally.
Season with salt and pepper. Bake until onions
are dark brown on
bottom, about 35 minutes.
Meanwhile, boil broth in heavy large skillet over
high heat until
reduced to 1/2 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 1 day
ahead. Cover and refrigerate. Rewarm over low heat
before continuing.
Cook green beans in large pot of boiling salted
water until
crisp-tender, about 5 minutes. Drain well. Return
beans to same pot.
Add remaining 2 tablespoons butter and toss to
coat. Mound beans in
large shallow bowl. Top with onion mixture and
serve.
