Preheat oven to 400 degrees F (200 degrees C).
Place squash and onion in a large skillet over medium heat. Pour in a small amount of water. Cover, and cook until squash is tender, about 5 minutes. Drain well, and place in a large bowl.
In a medium bowl, mix together cracker crumbs and cheese. Stir half of the cracker mixture into the cooked squash and onions. In a small bowl, mix together eggs and milk, then add to squash mixture. Stir in 1/4 cup melted butter, and season with salt and pepper. Spread into a 9×13 inch baking dish. Sprinkle with remaining cracker mixture, and dot with 2 tablespoons butter.
Bake in preheated oven for 25 minutes, or until lightly browned.