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.
Dot the butter over the top.
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.
Pour the broth and vinegar carefully into the pan, and return it to the oven for another 15 minutes, or until the garlic cloves are tender and the liquids have reduced.
Finish with a sprinkling of sea salt.
