Whisk together broth, vinegar, soy, sugar, cornstarch and sesame oil in bowl.
Stir-fry garlic and ginger in 1 teaspoon oil in nonstick skillet until softened and lightly browned, 2 minutes. Transfer garlic mixture to beef broth mixture in bowl.
Heat remaining oil in skillet. Add eggplant and green onion; stir-fry until eggplant and onion are just tender, about 8 minutes. Add tofu and radishes; add broth-garlic mixture. Stir gently over high heat until sauce boils and thickens. Serve immediately.