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Halve, core, and thinly slice the red cabbage.
Heat olive oil in a large skillet over medium heat. Add cabbage and red-wine vinegar; season with coarse salt and ground pepper.
Cook, tossing frequently, until cabbage is crisp-tender, about 15 minutes (add a splash of water if pan becomes dry).
Add light-brown sugar; toss until dissolved, about 30 seconds. Season again with salt and pepper, as desired before serving.
1 small head red cabbage (about 1 ½ pounds)
1 tablespoon olive oil
3 tablespoons red-wine vinegar
Coarse salt and ground pepper
2 tablespoons light-brown sugar