Preheat oven to 350°F and grease a 9x13-inch baking dish.
Cook egg noodles according to package directions until al dente, then drain and set aside.
In a large bowl, combine cream of mushroom soup, sour cream, chicken broth, thyme, and black pepper, whisking until smooth.
Stir in the cooked noodles, turkey, peas, Swiss cheese, and cheddar cheese until everything is well combined.
Pour mixture into the prepared baking dish and spread evenly.
In a small bowl, toss crushed Ritz crackers with melted butter until well coated.
Sprinkle the buttered crackers evenly over the top of the casserole.
Bake for 30-35 minutes until the topping is golden brown and the casserole is bubbling around the edges, then let cool for 5 minutes before serving.