Wash the yellow squash and zucchini under cool water, then slice them into thin rounds, about 1/4 inch thick.
In a large skillet, heat olive oil over medium heat. Add the sliced yellow squash, zucchini, and diced onion. Sauté for 5-7 minutes until tender.
In a large mixing bowl, combine the sautéed vegetables with shredded cheddar cheese, crushed buttery crackers, beaten eggs, and milk. Mix until well combined.
Pour the mixture into a greased 9x13-inch baking dish and spread it out evenly. Sprinkle grated Parmesan cheese on top.
Bake in a preheated oven at 350°F for 25-30 minutes until set and golden brown. Allow to cool for 5 minutes before serving.