Coat a large nonstick skillet with cooking spray; heat over medium-high heat. Add eggplant, onion and carrots; cook, stirring occasionally, until vegetables soften slightly and are light golden, 7 minutes.
Add beef to skillet; cook until browned, breaking up clumps with a wooden spoon, 2 minutes. Stir in garlic, cumin and cinnamon; cook until fragrant, stirring, 30 seconds.
Stir in tomatoes, chickpeas, broth, apricots and salt; bring to a boil over medium-high heat. Reduce heat to medium-low; simmer, stirring occasionally, for vegetables to become tender and for flavors to develop, 10 minutes. Remove from heat; stir in cilantro and serve with lemon wedges.