Preheat your oven to 350°F (175°C).
In a skillet, sauté the sliced squash and chopped onion in 1 tablespoon of butter over medium heat for 5 to 7 minutes, or until the vegetables are softened.
Transfer the cooked squash mixture to a large mixing bowl. Add the shredded cheddar cheese, sour cream, salt, pepper, and beaten egg. Stir until everything is evenly combined.
Pour the squash mixture into a greased 8x8-inch baking dish and spread evenly.
In a small bowl, mix the crushed crackers with the melted butter. Sprinkle this buttery crumb topping evenly over the casserole.
Bake for 25 to 30 minutes, or until the topping is golden and the casserole is bubbly.
Let cool for 5 minutes before serving.