Combine first 2 ingredients in large pot and bring to boil. Reduce heat to medium, cover and simmer.
Add potatoes and apples to pot. Cover; simmer until very tender, about 20 minutes. Remove from heat. Using slotted spoon, transfer potatoes and apples to large bowl; add 3 tablespoons butter and toss with with salt and pepper. Pour broth mixture from pot into medium bowl; reserve pot.
Sprinkle chicken with salt, pepper and 4 teaspoons thyme; dust with flour. Melt remaining 2 tablespoons butter in reserved pot over medium-high heat. Add half of chicken. SautÃ© until brown and cooked through, turning with tongs, about 5 minutes. Using slotted spoon, transfer sautÃ©ed chicken to 11x7x2-inch baking dish. Repeat with remaining chicken. Add potato-apple mixture.
Return broth mixture to same pot; Boil over medium-high heat until sauce is reduced to 1 1/4 cups, scraping up browned bits, about 3 minutes. Season with salt and pepper. Spoon over chicken.
Preheat oven to 350F. Bake casserole uncovered until potato topping is crusty and chicken filling is heated through, about 35 minutes (about 45 minutes if refrigerated).