Preheat your oven to 400 degrees.
Place squash and onion in a large skillet and pour in enough water to cover. Turn the heat on medium-high, cover, and cook until tender – about 5-10 minutes, depending on how tender you like your squash.
Drain well to remove excess water, and pat dry with paper towels to prevent a watery casserole. Set aside.
In a small bowl, whisk together the eggs, milk, salt, & pepper.
In another bowl, mix together the crumbled cheese crackers with the butter and then add the shredded cheese.
Stir half of the crumb mixture into the squash along with the egg mixture. Combine well. Pour into a 2 to 3 quart casserole dish, and top with the remaining cracker/cheese mixture. Bake for 30 minutes.