Preheat oven to 475°F (245°C). In a large bowl, toss cabbage wedges with olive oil, kosher salt, and pepper until evenly coated. Arrange them in a single layer on a rimmed baking sheet and dot with butter pieces. Roast for 12–15 minutes or until edges develop deep brown spots.

Using a spatula, turn each wedge, tuck smashed garlic cloves among the cabbage, and return the pan to the oven. Roast for another 12 minutes, until both sides are richly charred.

For extra crisp, switch to broil for 2–3 minutes, watching closely to prevent burning. Alternatively, place the sheet pan on medium-high stovetop heat.

Carefully pour in vegetable broth and white vinegar. Stir gently to coat cabbage and garlic. Return to oven or keep on stovetop for 5–7 minutes, until the vinegar-broth mixture is nearly evaporated and flavorful juices cling to the cabbage.

Transfer to a serving dish, sprinkle with flaky sea salt, and enjoy immediately so the edges remain crunchy.