Preheat oven to 425°F. Combine Brussels sprouts and onion in medium bowl with 3 tablespoons of the olive oil, salt and pepper, tossing gently. Spread on lightly greased baking sheet; roast 25 to 30 minutes or until vegetables are tender and caramelized.
Meanwhile, sauté shallot in remaining olive oil in small skillet over medium-high heat 5 minutes or until tender. Add balsamic vinegar and cook 5 minutes more. Stir in rosemary and pour over Brussels sprouts.
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