1. Position a rack about 6-inches from broiler and heat to high. Bring a medium-large pot of salted water to a boil. Add the pasta and cook, stirring often, until al dente, about 10 minutes. Drain well and rinse under cold running water. Spread out on paper towel to absorb excess moisture.
2. Meanwhile, put the tomatoes in a small bowl and stir in 1 tablespoon vinegar, 1 tablespoon olive oil, and 1/4 teaspoon salt. Set aside to macerate for 15 to 20 minutes.
3. Arrange the peppers on a broiling pan, cut side down and broil, until blistered and black in spots, 5 to 7 minutes. Transfer peppers to a bowl, cover with a lid or plate and set aside to steam for 10 to 15 minutes. Rinse or scrape off the skin; cut peppers into a dice.
4. Mix the remaining 1 tablespoon vinegar, mustard in a large bowl, season with 1/2 teaspoon salt and some pepper. Whisk in the remaining 2 tablespoons olive oil until smooth. Add the tomatoes with accumulated juices, the roasted peppers, and parsley and toss lightly. Just before serving, add the chicken and pasta and toss gently until combined. Season with salt and pepper. Serve.
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