Technically yes, you can, although you might not need to according to Jamie Simpson, the executive chef liaison at The Culinary Vegetable Institute. "Since a head of fresh cabbage can last for four ...
Once cut, cabbage can dry out and spoil more quickly, so it's important to take care when storing cut or shredded cabbage.
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Can you freeze cabbage?

Cabbage can be frozen raw or blanched, but blanching extends its freezer life up to 9 months. Blanched cabbage maintains its flavor and texture better than raw when frozen. Proper packaging is crucial ...