Preheat oven to 350°. Spray a 2-quart baking dish with cooking spray.
In a large saucepan, bring broth to a boil over medium-high heat. Add zucchini, squash, and onion. Reduce heat and simmer until crisp-tender, about 4 minutes. Drain. Wipe pan.
In the same saucepan, melt butter over medium heat. In a small bowl, toss together 1 tablespoon melted butter, bread crumbs, and ¼ teaspoon salt. Set aside.
Whisk flour into remaining 3 tablespoons butter in saucepan, whisking for 1 minute. Whisk in milk; bring to a gentle boil over medium-high heat, whisking constantly. Reduce heat to medium-low. Cook until thickened, stirring constantly, 2 to 3 minutes. Add pepper, cheese, basil, and remaining 1 teaspoon salt, whisking until smooth.
Spread zucchini mixture into prepared dish and top with cheese sauce. Sprinkle bread crumbs mixture over top.
Bake until bubbly and golden, about 25 minutes.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/zucchini-and-squash-gratin-recipe/