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Preheat the oven to 400 degrees.
Place the whole peppers, including the stems, in a single layer in a large (or two smaller) ceramic baking dish. Drizzle with 4 tablespoons olive oil, sprinkle with 2 teaspoons salt and 1 teaspoon pepper, and toss well. Lay the sprigs of thyme on top and roast for 20 to 25 minutes, until the peppers start to brown in places but are not blackened. Discard the thyme sprigs.
While still hot, drizzle the peppers with 3 tablespoons of balsamic vinegar and season to taste. Serve warm or at room temperature.