Preheat the oven to 375°F. Lightly grease a 9x13-inch baking dish.
In a large bowl, combine the cream of chicken soup, sour cream, milk, garlic powder, onion powder, thyme, salt, and black pepper. Stir until smooth.
Add the cooked chicken, mixed vegetables, and 1 cup of shredded cheddar cheese. Stir until everything is evenly coated with the creamy mixture.
Spread the chicken mixture evenly in the prepared baking dish.
Sprinkle the remaining 1 cup of cheddar cheese evenly over the top.
Combine the crushed crackers with the melted butter in a small bowl. Sprinkle the mixture over the cheese.
Bake uncovered for 25–30 minutes, or until the filling is bubbling around the edges and the topping is golden.
Remove from the oven and let the casserole rest for 5–10 minutes before serving.