1. Preheat oven to 425°.
2. Place beans into a large saucepan of boiling water; cook 4 minutes. Drain and rinse with cold water; drain well. Place beans in a large bowl; set aside.
3. Heat a large skillet over medium-high heat. Add oil to pan; swirl to coat. Add onion and thyme to pan; sauté 4 minutes or until onion is tender, stirring occasionally. Add mushrooms; sauté 10 minutes or until liquid almost evaporates, stirring frequently. Stir in wine, salt, and pepper; cook 2 minutes or until liquid almost evaporates. Stir in flour; cook 1 minute, stirring constantly. Gradually stir in chicken broth; bring to a boil. Cook 1 minute or until thick, stirring constantly. Add mushroom mixture to green beans; toss well. Place green bean mixture in a 2-quart glass or ceramic baking dish. Combine fried onions and grated cheese in a small bowl. Top green bean mixture evenly with fried onion mixture. Bake at 425° for 17 minutes or until top is lightly browned.