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1
Soak beans in cold water to cover by 2 inches in a bowl at room temperature at least 8 hours, or quick-soak (see cooks' note, below).
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2
Drain in a colander.
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3
Pat shanks dry and sprinkle with pepper and 1 teaspoon salt.
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4
Heat oil in a wide 6- to 8-quart heavy pot over moderately high heat until hot but not smoking, then brown shanks (in batches if necessary), turning, about 6 minutes total, and transfer with tongs to a bowl.
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5
Cook onion in fat remaining in pot over moderate heat, stirring, until golden, about 5 minutes.
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6
Add garlic and cook, stirring, 1 minute.
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7
Add browned meat along with any juices accumulated in bowl, carrots, 8 cups water, beef broth, and remaining 1/2 teaspoon salt and simmer, covered, until meat is very tender, about 1 1/2 hours.
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8
Remove shanks with a slotted spoon and transfer to a cutting board.
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9
When cool enough to handle, cut meat into 1-inch pieces, discarding bones, and return meat to soup.
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10
Meanwhile, simmer lima beans in remaining 4 cups water in a 4-quart saucepan, covered, until just tender, 20 to 30 minutes.
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11
Drain in colander.
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12
Peel potatoes and cut into 1-inch cubes, then add to soup with lima beans and tomatoes with their juice and simmer, covered, until potatoes are tender, about 15 minutes.
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13
Add cabbage and green beans and simmer, uncovered, until tender, about 5 minutes.
