Preheat oven to 400°F. Combine chicken, green beans, 1 tablespoon oil and ½ teaspoon each salt and pepper in a 9-by-13-inch baking dish; toss to coat and spread in an even layer. Roast until the beans are browned in spots and an instant-read thermometer inserted into thickest portion of chicken registers 165°F, about 30 minutes. Spoon out all liquid from the baking dish, reserving the chicken mixture.
Meanwhile, heat the remaining 2 tablespoons oil in a large skillet over medium heat until shimmering. Stir in sliced mushrooms and onion; cook, undisturbed until the mushrooms are golden brown on the bottom, 3 to 4 minutes. Stir once, add garlic and cook, stirring often, until fragrant, about 1 minute. Stir in 2 teaspoons sherry, gently scraping the browned bits from the bottom of the pan.
Add 1 (10.5-ounce) can cream of mushroom soup, ½ cup cream and ½ teaspoon each oregano and thyme; cook, stirring constantly, until the mixture slightly thickens, about 1 minute. Remove from heat; stir in 3 tablespoons Parmesan until combined.
Add the mushroom mixture to the chicken mixture in the baking dish; stir to combine, then spread in an even layer. Top with 1¼ cups fried onions and the remaining 3 tablespoons Parmesan. Bake at 400°F until the casserole is warmed through and the cheese is melted, 4 to 5 minutes.
