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Preheat oven to 425°F. Arrange cabbage wedges in a single layer on a large rimmed baking sheet. Whisk 3 tablespoons oil, 1 teaspoon mustard, 1 teaspoon garlic powder and ¼ teaspoon salt together in a small bowl. Brush the mixture over the cut sides of the cabbage wedges. Roast until browned on the edges, 18 to 20 minutes.
Meanwhile, whisk 2 tablespoons vinegar and the remaining 1 tablespoon oil, 2 teaspoons mustard and ¼ teaspoon salt together in a small bowl until combined.
Remove the cabbage from the oven; brush the wedges with half of the balsamic mixture. Flip the wedges and brush with the remaining balsamic mixture. Roast until the cabbage is tender and the balsamic mixture has started to thicken and caramelize around the edges, about 15 minutes. Transfer to a large platter. Sprinkle with ½ cup goat cheese and 2 teaspoons thyme.