Preheat oven: Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish.
Cook the filling:In a large skillet, melt the butter over medium heat. Add onions and garlic, cooking until soft and fragrant (about 2–3 minutes).
Add vegetables:Stir in frozen vegetables and cook for another 3–4 minutes until they begin to soften.
Make the sauce: Sprinkle flour over the veggies and stir well to coat. Gradually whisk in chicken broth and milk. Simmer until thick and creamy (about 5–6 minutes).
Combine everything: Stir in shredded chicken, salt, pepper, thyme, and cheese (if using). Remove from heat.
Assemble the casserole:Pour the creamy chicken mixture into the prepared baking dish. Arrange biscuit dough or puff pastry on top to cover.
Bake:Brush the top with melted butter and bake for 25–30 minutes, or until the topping is golden brown and the filling is bubbling.
Serve and enjoy: Let cool slightly before serving. Garnish with parsley if desired!