Prepare the Vegetables. Start by slicing the zucchini and yellow squash into thin rounds. Finely chop the onion and mince the garlic.
Saute the Vegetables. In a large skillet, heat a tablespoon of olive oil over medium heat. Add the chopped onion and minced garlic. Saute until they become translucent and fragrant.
Add Zucchini and Squash. Add the sliced zucchini and yellow squash to the skillet. Cook for about 5-7 minutes, or until they begin to soften. Season with salt, black pepper, dried oregano, and dried basil. Stir occasionally to ensure even cooking.
Prepare the Casserole Mixture. In a separate mixing bowl, combine the shredded cheddar cheese, grated mozzarella cheese, sour cream, mayonnaise, and eggs. Mix until all ingredients are well combined.
Combine the Elements. Once the zucchini and squash are tender, remove them from the heat. Let them cool for a few minutes. Then, gently fold the sauteed vegetables into the cheese and sour cream mixture until everything is evenly coated.
Layer and Bake. Preheat your oven to 350°F. Grease a baking dish (9x13 inches or a similar size). Pour the zucchini and squash mixture into the dish and spread it out evenly.
Bake to Perfection. Place the casserole in the preheated oven and bake for 25-30 minutes, or until the top is golden brown and the casserole is bubbling around the edges.
Serve and Enjoy. Remove the casserole from the oven and allow it to cool slightly before serving. It's best enjoyed warm.