Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
In a large skillet over medium heat, melt butter. Add the diced onion and cook for 3–4 minutes until soft and translucent. Stir in the garlic and cook for another minute.
Add the frozen vegetables and cooked potatoes (if using). Cook for 3–5 minutes until heated through. Stir in the shredded chicken.
Add the cream of chicken soup, sour cream, milk, salt, pepper, and thyme. Stir everything together and simmer for 2–3 minutes until well combined and creamy.
Pour the filling mixture into the prepared baking dish and spread evenly. Top with biscuit dough pieces—either place whole biscuits on top or cut into quarters and scatter them evenly.
Optional: Sprinkle shredded cheese over the biscuits for a golden, cheesy crust.
Bake uncovered for 25–30 minutes or until the biscuits are golden brown and cooked through. Let the casserole rest for 5 minutes before serving.