Slice a cabbage in half through the stem. Place cut side down. In the same direction as the stem, cut ¼ - ½” slices so that you have ribbons of cabbage. Discard the stem.
Preheat a large skillet over medium heat. Add a drizzle of olive oil and a tablespoon of butter. Once the butter has melted, add the sliced cabbage. Stir gently to coat in butter. Allow to cook undisturbed until the cabbage begins to soften, about 5 minutes. Add salt and pepper.
Lower heat to medium-low. Continue cooking, stirring occasionally, until the cabbage is wilted and tender. Increase heat to medium, add 1 tablespoon of butter, and allow cabbage to cook undisturbed until some pieces begin to turn brown and caramelize.
Remove from heat. Add a splash of apple cider vinegar. Stir to combine. Add salt and pepper to taste. Serve warm.