processes for producing a nutritional supplement that contains sulforaphane , and supplements formed thereby . such a process includes combining a cruciferous vegetable , for example , broccoli sprouts , with at least one strain of lactobacillus to form a mixture , causing the mixture to undergo lactic fermentation , transform a glucosinolate within the cruciferous vegetable to sulforaphane , and yield a fermented mixture that contains sulforaphane , and then producing from the fermented mixture a supplement that can be ingested by an individual .