Begin by halving the cabbage from the top down through its core. Place one half cut-side down on your cutting board and slice it thinly around the core to create fine ribbons, discarding the core afterward.

Heat a large sauté pan or heavy-bottomed pot over medium-high heat. Add olive oil and butter to the pan, allowing the butter to melt completely.

Once the butter is melted, add the sliced cabbage to the pan, along with salt and pepper. Sauté the cabbage for approximately 10 to 15 minutes, stirring occasionally, until it becomes tender and starts to brown. It's important not to over-stir; allowing the cabbage to sit undisturbed for a minute or two will help develop flavorful caramelized bits.

Once the cabbage is cooked to your desired tenderness and has developed some caramelization, remove the pan from the heat.

Stir in the apple cider vinegar, adjusting the seasoning with additional salt, pepper, or vinegar to taste for a vibrant and acidic flavor profile.

Sprinkle the sautéed cabbage with thyme before serving, and enjoy it warm alongside your favorite dishes.