LeRoy and Lewis Barbecue sells pork hash.

The history of American cuisine — and barbecue in particular — is, at its core, a story about what to do with leftovers.

Not the modern-day kind, like the turkey sandwiches and casseroles we cobble together after Thanksgiving. Those are recent creations. The leftovers that shaped our foodways are the remnants left behind after we carve off the most desirable parts of an animal: the ribs, chops and shoulders everyone wants. What, then, do we do with the organs, fat and skin?

GUIDE: The best barbecue in Houston

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Today we live in a land of abundance, but that wasn’t always true. A century ago, food scarcity was a real concern. To avoid waste, cooks were challenged to make every part of an animal or plant not just edible, but........

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