Preheat oven to 350°F. Lightly grease a 3-qt. baking dish. In a large Dutch oven, combine squash, broccoli, carrot, onion, and water to cover; bring to a boil over high heat. Reduce heat, and simmer for 10 to 12 minutes, or until vegetables are tender. Drain well.
In a large bowl, combine vegetable mixture, cheese, and butter, stirring until melted. Add sour cream, soup, eggs, salt, and pepper, stirring until combined. Add Ritz crackers; stir well. Spoon mixture into prepared baking dish.
Bake for 20 minutes. Sprinkle casserole evenly with onion rings. Bake for 10 to 15 minutes longer, or until hot and bubbly.