A hit under the broiler leaves zucchini perfectly tender.
Preheat broiler to high.
Combine 1/4 cup tzatziki, breadcrumbs, onion, 3 tablespoons mint, cumin, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and red pepper in a bowl, stirring with a whisk. Add chicken; mix with hands. Shape chicken mixture into 8 patties. Heat 2 teaspoons olive oil in a nonstick skillet over medium heat. Add patties; cook 4 minutes on each side or until done.
While kofte cook, arrange zucchini, cut side up, on a jelly-roll pan coated with cooking spray. Brush with remaining 2 teaspoons oil; sprinkle with the remaining 1/8 teaspoon salt and 1/8 teaspoon black pepper. Broil 5 minutes or just until tender. Divide kofte and zucchini among 4 plates. Sprinkle with remaining 2 tablespoons mint. Serve with remaining 1/4 cup tzatziki.