Answer: You probably have a type of Alocasia which spreads by rhizomes -- and looks very similar to the related Colocasia; both are commonly called elephant ear or taro.
To save it for next year, you could try potting up some rhizomes and keeping them as houseplants for the winter. You may also have success storing them just as you do the tubers. Gardeners report success using both methods so I would suggest you try both and see which one works better for you.
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