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Step 1
Cut the cabbage in half from its top down through its core. Place the cut-side down on your cutting board, then slice it as thinly as possible around the core so that you have fine ribbons. Discard the core.
Step 2
Heat a large saute pan or similar heavy-bottomed pot over medium-high heat. Add olive oil and butter. Once the butter is melted, add the cabbage, salt, and pepper. Saute for 10 to 15 minutes, stirring occasionally, until the cabbage is tender and begins to brown. Don't feel like you need to constantly stir it. Leaving cabbage undisturbed for a minute or two as you go is what will allow it to develop brown caramelized bits (aka FLAVOR).
Step 3
Remove from the heat and stir in the apple cider vinegar. Taste and add a bit of additional salt and pepper if you like, or a splash more vinegar if you'd like to add more zippy and acidic flavors. Sprinkle with thyme. Serve warm.