1. Heat a large skillet over medium-high heat. Add oil to pan; swirl to coat. Add onion and next 3 ingredients (through jalapeño); sauté 4 minutes. Add garlic; sauté 1 minute. Stir in tomato paste and 1 cup broth. Transfer vegetable mixture to a 5-quart electric slow cooker.
2. Stir in remaining 3 cups broth, thyme, and next 6 ingredients (through black beans). Cover and cook on LOW for 8 hours.
3. Stir in coconut milk. Ladle soup into bowls; top with cilantro. Serve with lime wedges.