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How to mince a shallot
Lay the shallot on your cutting board.
Position your knife above the end of the shallot that has the small rootlets.
Cut a slit that is deep enough to almost but not quite cut off the end.
Leaving the end barely attached will make the shallot easier to peel. Position the shallot so that the rootlet end is on top and the wide end is on bottom.