Heat oil in a large nonstick skillet over medium heat. Add onion and carrot; cover and cook 5 minutes or until tender. Add curry powder, sugar, ginger, garlic, and chile; cook 1 minute, stirring constantly.
Place onion mixture in a 5-quart electric slow cooker. Stir in chickpeas and next 8 ingredients (through broth). Cover and cook on HIGH 6 hours or until vegetables are tender. Add spinach and coconut milk; stir until spinach wilts. Serve with lemon wedges.