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Remove any bruised or damaged outer leaves from the cabbage. Rinse and dry the surface before cutting. Securely hold the cabbage and carefully cut it down through the stem to create two halves. Place them cut-side down on the cutting board. Then cut each half into quarters by cutting down through the stem. Carefully remove the thick cores with a knife. Cut the quarters into ½-inch thick slices. There should be about 20 cups (2 ½ pounds, 1.14kg) of shredded cabbage.
Heat a large 12-inch skillet or dutch oven over medium heat. Add the olive oil and butter. Once the butter melts, add the onions. Saute and stir occasionally until the surface lightly browns and the onions are translucent, about 7 minutes.
Add the garlic and saute until fragrant, 30 seconds.
Add half of the cabbage, stir and cook until it begins to wilt and reduce in volume, about 2 minutes. Add the remaining cabbage and stir until wilted, 2 minutes. Continue to cook for 8 minutes, stirring every minute to allow lightly even browning.
Add the apple cider vinegar, stir and cook for 1 minute.
Add the salt and pepper, stir and cook for 1 minute. Season to taste. Garnish with sliced green onions and serve hot.