Preheat the oven to 375°F (190°C). Grease a 9x13-inch baking dish.
In a large skillet, heat a tablespoon of oil over medium heat. Add the chopped onion and minced garlic, and sauté until softened and fragrant, about 5 minutes.
In a large mixing bowl, combine the cooked and shredded chicken, steamed broccoli florets, sliced mushrooms, and frozen peas.
In a separate bowl, mix together the condensed cream of chicken soup, sour cream, mayonnaise, shredded cheddar cheese, grated Parmesan cheese, milk, dried thyme, dried oregano, salt, and pepper. Stir until well combined.
Pour the creamy mixture over the chicken and vegetables, and mix until everything is evenly coated.
Transfer the mixture to the greased baking dish and spread it out evenly.
In a small bowl, mix the crushed Ritz crackers or breadcrumbs with the melted butter. Sprinkle the mixture evenly over the top of the casserole.
Bake in the preheated oven for 30-40 minutes, or until the casserole is bubbly and the top is golden brown.
Remove from the oven and let cool slightly before serving.
Garnish with fresh parsley and enjoy your Ultimate Chicken Casserole!