In a large skillet cook onions, covered, in hot oil over medium-low heat for 13 to 15 minutes or until onions are tender. Uncover; add brown sugar. Cook and stir over medium-high heat for 3 to 5 minutes or until onions are golden and caramelized. Set aside.

Preheat oven to 400 degrees F. In a large saucepan cook green beans, covered, in a small amount of boiling water for 3 minutes. Drain. In a 3-quart au gratin or baking dish combine green beans and mushrooms. Combine olive oil, soy sauce, and balsamic vinegar. Pour over vegetables, tossing to coat. Roast for 15 to 20 minutes, stirring once, until crisp tender.

Meanwhile, in a medium mixing bowl beat together cheese and milk with an electric mixer on medium speed. Spoon cheese in lengthwise mounds along center of baking dish. Top with caramelized onions. Return to oven; heat 5 to 8 minutes or until cheese and onions are heated through. Makes 10 to 12 servings.

Test Kitchen Tip: To make ahead, prepare onions as directed in Step 1; refrigerate until ready to assemble. Prepare vegetables and mushrooms as directed in Step 2; refrigerate until ready to assemble. Remove onions and vegetables from refrigerator 30 minutes before using. To reheat, assemble dish as directed in Step 3, omitting cheese mixture. Heat in a 400 degree F. oven for 30 minutes. The last 5 minutes of baking time, spoon cheese mixture over onions.