In a large Dutch oven, heat oil over medium-high until shimmering. Add onion and carrots. Cook, stirring occasionally, until softened, 3 to 5 minutes. Stir in garlic, ginger, cumin, pepper, turmeric, and smoked paprika, and cook until fragrant, about 1 minute. Add cabbage and cook, stirring often, until cabbage turns bright green, about 2 minutes.
Stir in broth, chickpeas, diced tomatoes, cauliflower, and salt. Bring mixture to a boil over high heat. Reduce heat to a simmer and cook, stirring occasionally, until cabbage and cauliflower are tender, 25 to 30 minutes.
Stir in coconut milk and return to a simmer. Cook, stirring occasionally, until warmed through, about 2 minutes. Divide soup among serving bowls and top with cilantro. Serve with lime wedges.
