1. Combine soy sauce and 1 teaspoon sugar in medium bowl. Add beef, toss well, and marinate for at least 10 minutes or up to 1 hour, stirring once. Meanwhile, whisk remaining 2 tablespoons sugar, lime juice, chicken broth, coconut milk, fish sauce, and cornstarch in medium bowl. Combine garlic, curry paste, and 1 teaspoon oil in small bowl.

2. Drain beef and discard liquid. Heat 1 teaspoon oil in 12-inch nonstick skillet over high heat until just smoking. Add half of beef to skillet in single layer, breaking up any clumps. Cook, without stirring, for 1 minute, then stir and continue to cook until beef is browned, 1 to 2 minutes. Transfer beef to clean bowl. Heat 1 teaspoon oil in skillet and repeat with remaining beef. Rinse skillet clean and dry with paper towels.

3. Add remaining tablespoon oil to now-empty skillet and heat until just smoking. Add eggplant and cook, stirring frequently, until browned and no longer spongy, 5 to 7 minutes. Push eggplant to sides of skillet to clear center; add garlic-curry mixture to clearing and cook, mashing with spatula, until fragrant, 15 to 20 seconds. Stir to combine garlic-curry mixture with eggplant. Return beef and any accumulated juices to skillet and stir to combine. Whisk sauce to recombine, then add to skillet along with basil leaves; cook, stirring constantly, until sauce is thickened and evenly distributed, about 30 seconds. Transfer to serving platter and serve, passing lime wedges separately if using.

Serves 4 as a main dish with rice