1. Cook the green beans in boiling water for 2 minutes. Drain and rinse with cold water, and drain well.
2. Place walnuts in a large nonstick skillet; cook over medium heat 7 minutes or until lightly browned, shaking pan frequently. Remove walnuts from pan; set aside. Add 4 teaspoons oil to pan; swirl to coat. Add onion and thyme to pan; cook 17 minutes or until onion is very tender and golden brown, stirring occasionally. Remove onion mixture from pan; keep warm.
3. Return pan to medium-high heat. Add remaining 2 teaspoons olive oil to pan; swirl to coat. Add green beans; cook 2 minutes or until thoroughly heated, stirring frequently. Add onion mixture and vinegar to pan; cook 2 minutes or until thoroughly heated, tossing to combine. Remove from heat. Sprinkle with nuts, salt, and pepper. Serve immediately.