Preheat oven to 375°F (190°C) and butter a 9x13-inch baking dish.
Boil linguini in salted water, 1 minute less than the package suggests. Drain and set aside.
In a large bowl, whisk together cream of chicken soup, cream cheese, garlic, sour cream, chicken broth, parsley, garlic powder, black pepper, and salt until smooth.
Stir in half of the mozzarella and cheddar. Fold in shredded chicken and cooked pasta until evenly coated.
Transfer mixture to prepared dish and top with remaining cheese.
Bake for 30–35 minutes, until the top is golden and bubbly.
Let cool slightly before serving for the creamiest texture.