Preheat oven to 350 degrees. Grease a roasting pan.

Cut cabbage in half lengthwise, drizzle ½ tablespoon olive oil on each cut side, spread it out, sprinkle with salt, and place cut side down on the roasting pan. Drizzle ½ tablespoon oil on each round side, spread it out, and sprinkle with salt.

Roast cabbage for 30 minutes.

Flip the cabbage so the cut side is up, drizzle 1 tablespoon oil and 1-2 tablespoons balsamic vinegar into the layers of the cut side, sprinkle with salt, and return to the oven for another 1½ hours until very tender.

Let cabbage stand for 10 minutes, covered lightly with aluminum foil, and serve.