Preheat the oven to 350°F and lightly grease a 13x9-inch baking dish with softened butter or spray with cooking spray.
In a large mixing bowl, beat the softened cream cheese, sour cream and mayonnaise with an electric mixer on medium-high speed until smooth.
Add the cream of chicken soup, granulated garlic, seasoned salt, black pepper, onion powder, smoked paprika and thyme. Stir until well blended.
Fold in the shredded chicken and 1 1/2 cup shredded cheddar cheese and 1/2 cup monterey jack cheese, making sure it's evenly distributed and coated with the creamy mixture. (Toss together the remaining 1/2 cup cheddar cheese and 1/2 cup monterey jack cheese for the top.)
Spread the chicken mixture evenly into the prepared baking dish. Top with the reserved 1 cup cheese.
In a small bowl, combine crushed Ritz crackers with melted butter and Parmesan cheese until well coated. Sprinkle the cracker mixture evenly over the casserole.
Lay a piece of foil on top. Bake in the preheated oven for 20 minutes. Remove the foil and bake for another 15-20 minutes until the top is golden brown and the filling is bubbling.
Allow the casserole to rest for 5 minutes before sprinkling with fresh parsley and serve with rice, mashed potatoes or egg noodles.