Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with cooking spray or butter.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté for about 3-4 minutes until translucent.
Add the sliced yellow squash and zucchini to the skillet. Season with salt, black pepper, and garlic powder. Cook for another 5-7 minutes until the squash is tender. Remove from heat and let cool slightly.
In a large bowl, combine the cooked rice, cheddar cheese, Parmesan cheese, eggs, milk, and chopped basil. Mix well.
Stir in the sautéed squash mixture until everything is evenly combined.
Pour the mixture into the prepared baking dish and spread it evenly.
In a small bowl, mix the panko breadcrumbs with the melted butter. Sprinkle the breadcrumb mixture evenly over the casserole.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown and the casserole is set. Let it cool for 5-10 minutes before serving.