Preheat oven to 350°F. Cover bottom of 13x9-inch baking dish with melted butter.
Place shredded chicken and vegetables into baking dish; season with 1 teaspoon thyme, garlic powder, pepper, and salt. Pour soup, broth, and cream over casserole and stir until well combined.
Prepare biscuit mix according to package directions.
Drop 8 (about 1⁄4 cup each) biscuit dough portions onto chicken and vegetable mixture.
Bake, uncovered until biscuits are golden brown on top and casserole is bubbling around edges for 40 minutes. Sprinkle with remaining fresh chopped thyme.