Preheat oven to 350°. Cook yellow squash and sweet onion in boiling water to cover in a Dutch oven 8 minutes or just until vegetables are tender; drain squash mixture well.
Combine squash mixture, freshly shredded Cheddar cheese, next 5 ingredients, 1 cup breadcrumbs, and 3/4 cup Parmesan cheese. Spoon into a lightly greased 13- x 9-inch baking dish.
Stir together melted butter, French fried onions, and remaining 1 cup breadcrumbs and 1/2 cup Parmesan cheese. Sprinkle over squash mixture.