Cook tortellini according to package directions, omitting salt and fat; drain. Drain peppers, reserving 3 tablespoons liquid.
Arrange peppers, tortellini, broccoli, and next 3 ingredients on a large platter. Combine reserved pepper liquid, mustard, and olive oil; stir well. Drizzle mustard mixture over antipasto; serve immediately with breadsticks or, if desired, cover and chill.