Is the plant broccoli named after the italian name or does the italian name come from the plant?

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Is the plant broccoli named after the italian name or does the italian name come from the plant?
The word broccoli is originally Italian but it comes from the early Latin word "brachium." It is the plural of broccolo, which is the diminutive of brocco, meaning shoot, stalk. Broccoli is a cultivar of wild cabbage, remaining exactly the same species.