Preheat the oven to 375°F (190°C).

Melt 2 tablespoons of butter in a large skillet over medium heat. Add in the onion and sauté for about 3 to 5 minutes until soft and translucent.

Stir in 2 tablespoons of flour and cook for about 1 minute to make a roux. Gradually whisk in 1 cup of milk until the mixture thickens, about 2-3 minutes.

Add 2 cups of corn and 2 cups of diced yellow squash to the sauce. Season with salt and pepper, then fold in 3/4 cup of shredded cheddar cheese until melted.

Pour the mixture into a greased 9x13 inch baking dish and spread evenly.

Sprinkle the remaining 1/4 cup of shredded cheddar cheese and breadcrumbs on top, if desired.

Bake in the preheated oven for 25 to 30 minutes until bubbly and lightly golden brown.

Let the casserole rest for a few minutes before serving.