Preheat your oven to 350°F (180°C).
Lightly grease a 9x13-inch baking dish with olive oil.
In a large skillet, heat the olive oil over medium heat.
Add the sliced squash and chopped onion.
Cook until the squash is soft and the onion is translucent.
Drain any excess liquid from the squash and onion mixture.
Let it cool slightly.
In a large mixing bowl, combine the cooled squash and onion with the Cheddar, Monterey Jack, and Parmesan cheeses.
Add sour cream, mayonnaise, beaten egg, salt, and pepper to the mixture.
Mix until well combined.
Spread the mixture evenly into the prepared baking dish.
In a separate bowl, combine the crumbled crackers and melted butter.
Sprinkle over the top of the casserole.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown and the casserole is bubbly.
Serve hot and enjoy your Cracker Barrel Three Cheese Squash Casserole.