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In a deep heavy kettle cook bacon in 2 batches over moderate heat until crisp and transfer to paper towels to drain.
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Pour off all but about 3 tablespoons drippings and in drippings remaining in kettle cook onions, stirring occasionally, until browned slightly and softened. Transfer onions with a slotted spoon to a bowl.
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To kettle add broth, vinegar, brown sugar, red pepper flakes, and about half of bacon, stirring until sugar is dissolved.
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Add about half of collards, tossing until wilted slightly, and add remaining collards, tossing until combined.
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Simmer collards, covered, 30 minutes.
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Stir in onions and simmer, covered, 30 minutes more, or until collards are very tender.
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Serve collards topped with remaining bacon.