Preheat and Prepare: Preheat your oven to 350°F (175°C). Lightly coat a 9x13-inch baking dish with cooking spray or butter and set it aside for later use.

Cook the Onion: In a small skillet, melt 1 tablespoon of butter over medium heat. Incorporate the chopped onion and cook, stirring occasionally, until it becomes tender and translucent, which should take around 5 minutes.

Mix the Base: In a large bowl, combine the condensed cream of mushroom soup, milk, sour cream, sautéed onion, 6 ounces of shredded cheddar cheese (reserve the rest for topping), whisked eggs, and seasonings (garlic salt, salt, mustard powder, Italian seasoning, and pepper). Stir until well combined.

Add Vegetables and Rice: Fold in the frozen broccoli, mixed vegetables, and cooked rice into the creamy mixture. Stir until everything is evenly distributed.

Transfer to Baking Dish: Pour the vegetable and rice mixture into the prepared baking dish.

Top with Cheese and Crackers: Sprinkle the remaining shredded cheddar cheese over the top of the casserole. Sprinkle this mixture evenly over the cheese layer to create a crunchy topping.

Bake: Place the casserole in the preheated oven and bake for 30-35 minutes, or until the top is golden brown and the casserole is bubbling around the edges.

Serve: Let the casserole rest for 5-10 minutes before serving. Serve warm as a side dish or a hearty vegetarian main course.