Answer: Basil is a tender annual. It will continue to produce leaves as long as you keep the flower stalks cut down, and it doesn't experience a frost. Basil can be kept growing under greenhouse conditions - but if you cut it down and even if you insulate the roots, it may not live through the winter. Without leaves to manufacture food for the roots they will wither and die, as will they if exposed to cold temperatures. Keeping that in mind, if you'd like to try to keep your basil producing, go ahead and experiment.
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