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