Preheat the oven to 350 degrees. Coat the bottom of a 13×9-inch baking dish with melted butter.
Place shredded chicken and vegetables into the dish; season with thyme, pepper, and salt. Pour over condensed soup, broth, and cream; stir until well combined.
Prepare biscuit mix according to package instructions.
Drop 8 (about 1/4 cup) biscuit dough portions onto chicken and vegetable mixture.
Bake in the preheated oven, uncovered, until biscuits are golden brown on top and casserole is bubbling around the edges, about 40 minutes. Sprinkle with thyme.
