Combine vinegar, 2 teaspoons oil, salt, and pepper in a small bowl.
Cook beans in boiling water 2 minutes or until crisp-tender. Drain and plunge beans into ice water; drain.
Heat 1 teaspoon olive oil in a large nonstick skillet over medium-high heat. Add mushrooms to pan; sauté 7 minutes or until liquid evaporates. Add onions; sauté 1 minute. Add beans; sauté 3 minutes or until thoroughly heated. Remove from heat. Add vinegar mixture and hazelnuts to bean mixture, tossing to coat.