Preheat oven to 375 degrees F. Spray a 9x13-inch baking dish with nonstick cooking spray.
In a large bowl, whisk together the cream of chicken soup, skim milk, sour cream, chicken broth, garlic powder, onion powder, thyme, salt, and pepper.
Stir in the chicken, frozen vegetables, and 1/2 cup of the shredded cheese.
Pour the mixture into the prepared baking dish and spread evenly.
Unroll the crescent roll dough and gently pinch the perforated seams together to seal them, creating one solid sheet of dough.
Carefully place the dough over the top of the casserole, stretching it slightly if needed to cover the entire surface. Tuck or press the edges down around the sides of the dish.
Bake uncovered for 25–30 minutes, or until the filling is hot and bubbling and the crescent topping is golden brown.
Let the casserole rest for 5 minutes before serving.