Preheat oven to 425°F. Grease a 9 x 13-inch baking dish or spray with nonstick cooking spray; set aside.
In a large bowl, whisk together condensed soups, milk, chicken broth or water, thyme, salt, garlic powder, onion powder, and pepper. Stir in thawed broccoli, raw chicken, and uncooked pasta.
Transfer mixture to prepared baking dish. Cover tightly with foil and bake for 45 minutes.
Remove foil and give everything a stir in the dish. At this point, check to make sure that the pasta is al dente (tender, but with a firm bite). If it’s still too hard, cover again and return to the oven until the pasta is al dente.
Once the pasta is al dente, stir in the sour cream and then sprinkle the cheese over top.
Return to the oven and bake, uncovered, for 5-10 more minutes, or until pasta is tender, chicken is cooked through, and cheese is melted.