Preheat the oven to 350°F. Coat a 2- to 3-quart baking dish with cooking spray.
Melt ¼ cup butter (½ stick) in a large skillet over medium-high heat. Add the squash and onion and sprinkle with 1 teaspoon salt. Cover, and cook for 5 minutes, or until the vegetables begin to soften. Uncover, and cook for 5 to 10 minutes longer, or until the squash is tender.
Pour the squash and onions into a colander set over a bowl and let drain.
Meanwhile, mix together the sour cream, mayonnaise, eggs, Cheddar cheese, Parmesan cheese, 1 teaspoon salt, and ½ teaspoon pepper in a large bowl.
Add the squash and onions, folding gently to combine. Transfer to the prepared baking dish.
Melt the remaining butter and combine with the crushed crackers. Sprinkle evenly over the top of the squash.
Bake at 350°F for 30 to 35 minutes, or until the crackers are golden brown and the edges of the casserole are bubbly.