Yield: 4 servings
Heat your oven to 475°F (245°C).
On a rimmed 9-by-13-inch baking sheet, toss the cabbage with the olive oil, salt, and pepper to coat evenly, but leaving any chunks intact-that is, there’s no need to separate the leafy layers. Dot the butter over the top — it will melt in the oven. Roast for 15 minutes, until the cabbage is black in spots.
Use a spatula to turn the cabbage over and scatter the garlic cloves in the pan.
Return to the oven and roast for another 15 minutes, until the cabbage looks worrisomely charred (but it will be perfect, I promise). Pour the broth and vinegar carefully into the pan, and return it to the oven a final time, to roast for yet another 15 minutes, or until the garlic cloves are tender and the liquids have been reduced to a thin (or nonexistent) puddle. Finish with a sprinkling of sea salt, and good luck not eating the crunchy bits right from the pan.