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.