In 8 cup (2 L) round microwavable heatproof casserole, combine potatoes, carrots, onion and chicken broth. Cover and microwave at High for 10 to 12 minutes or until vegetables are almost tender, stirring twice during cooking. Stir in turkey, mushrooms, peas, soup, thyme and pepper until evenly combined, smoothing top. Set aside.
In small bowl, combine biscuit mix and parsley; stir in just enough milk to make a soft, sticky dough. Turn out onto floured surface and knead 6 to 8 times. Roll or pat into circle to fit casserole. Place dough on filling (don't worry if it falls apart, just pat together). Cut a few steam slits in topping.
Bake in preheated 400°F (200°C) oven until top is golden brown and filling is bubbly, 20 to 25 minutes. Let stand 5 minutes before serving.