Preheat your oven to 350°F (175°C). Grease a 2-quart baking dish with cooking spray or butter.
In a large skillet over medium heat, add the olive oil. Once hot, add the chopped onion and sauté for about 3 minutes until translucent.
Add the sliced yellow squash and zucchini to the skillet. Season with salt, pepper, and garlic powder. Cook for about 5-7 minutes, stirring occasionally, until the squash is tender. Remove from heat and let cool slightly.
In a large bowl, combine the beaten eggs, milk, and half of the cheddar cheese. Stir in the cooked squash mixture.
Pour the mixture into the prepared baking dish. Top with the remaining cheddar cheese and sprinkle the crushed crackers evenly over the top. Finish with the grated Parmesan cheese.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown and the casserole is set.
Remove from the oven and let cool for about 5 minutes before serving. Garnish with fresh parsley if desired.