Heat oven to 425°F (220°C). Remove any wilted outer leaves from the red cabbage, halve it through the core, then slice each half into 1 to 1½-inch wedges, keeping a bit of the core attached. Aim for 8 wedges.

In a small bowl, whisk together the olive oil, balsamic vinegar, garlic, salt, and black pepper until combined.

Place the wedges in a large bowl, pour the dressing over, and toss gently with your hands to coat evenly.

Arrange the wedges cut side down on a rimmed baking sheet and roast for 25 to 30 minutes, flipping halfway through, until deeply browned and fork-tender.

Transfer to a platter, spoon any pan juices over the top, and serve warm with an extra drizzle of balsamic if you like.