Preheat the Oven: Preheat your oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.
Sauté the Onion: In a large skillet, melt 1 tablespoon of butter over medium heat. Add the finely diced onion and sauté for 3-4 minutes until softened and translucent. Remove from heat and set aside.
Prepare the Creamy Sauce: In a large mixing bowl, whisk together the condensed cream of mushroom soup, milk, sour cream, and half of the shredded cheddar cheese (4 oz.).
Combine the Vegetables and Rice: Add the frozen broccoli, mixed vegetables, cooked rice, and whisked eggs to the creamy sauce mixture.
Season the Casserole: Add the garlic salt, salt, mustard powder, Italian seasoning, and black pepper to the vegetable mixture. Stir to incorporate the seasonings evenly throughout the mixture.
Assemble the Casserole: Pour the vegetable mixture into the prepared baking dish. Spread it out evenly. Top with the remaining shredded cheddar cheese (4 oz.).
Prepare the Topping: In a small bowl, mix the crushed Ritz crackers with the melted butter until well combined. Sprinkle the cracker mixture evenly over the top of the casserole.
Bake: Bake in the preheated oven for 30-35 minutes, or until the casserole is bubbly and the topping is golden brown.
Serve: Remove the casserole from the oven and let it cool for a few minutes before serving. Enjoy this comforting dish on its own or as a hearty side with your favorite protein.