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 bread crumbs and cheese. Stir half of the crumb 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 9x13 inch baking dish. Sprinkle with remaining bread crumb mixture, and dot with 2 tablespoons butter.Bake in 350 degree oven for 25 minutes, or until lightly browned.