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Wash you cabbage and take off the outside 3-4 leaves that are more rough or look unhealthy.
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Cut cabbage in half, than quarters.
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Using your mandolin on a thicker setting, shred each quarter of cabbage, carefully while watching your fingers. Mandolining (is that actually a thing?), is a dangerous business. If you don't have a mandolin, use your knife and slice it as thin as you can.
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In a cast-iron or non-stick skillet, add about 2 Tbsp of olive oil. Add the shredded cabbage to the skillet with about 1 tsp. of salt, cover it with a lid and turn heat on medium-low setting.
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Cook it for about 30-40 mins, and stirring occasionally until cabbage is soft. If you can't fit all cabbage in the skillet, after about 10 mins or once the cabbage cooks down a little bit, add the rest of it to the skillet.
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Meanwhile, cook the ground beef with 1/4 tsp of salt in a different skillet. Once cooked, add the beef to the cabbage and cook together for another 5 mins or until cabbage is tender.