In a large bowl, toss peppers, onion, and garlic with one tablespoon of the olive oil.
Arrange vegetables in a single layer on a baking sheet. Roast for 20 to 30 minutes or until peppers are browning on edges, stirring once halfway through. Return to bowl and allow to cool for 10 minutes.
Put cooled vegetables in a food processor with balsamic vinegar, remaining 2 tablespoons olive oil, parmesan cheese, salt, and pepper. Blend until smooth, adding more oil if necessary.