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Place leftover hambone in a large pot and cover with water halfway, about 6 cups of water.
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Bring to a boil. Reduce heat and simmer until very fragrant, about 30 minutes to 1 hour; remove and discard hambone.
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Heat olive oil in a large pot over medium heat.
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Add garlic, onion, carrots and potato. Cook, stirring occasionally, until onions become translucent, about 2-3 minutes. Stir in ham stock, beans and corn; season with salt and pepper, to taste.
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Bring soup to a boil; reduce heat and simmer until potatoes are tender, about 10-12 minutes. Stir in diced ham and serve warm.