Prepare the Aromatics: Heat vegetable oil in a large pot over medium heat. Add diced onion, crushed garlic, and finely chopped serrano pepper (if using). Cook for 5-7 minutes, stirring occasionally, until the onion softens and turns translucent.
Build the Tomato Base: Stir in tomato paste and cook for 1 minute. Add quartered tomatoes and cook for 3-4 minutes, stirring occasionally, until they soften slightly.
Add Vegetables: Incorporate sliced carrots and cooked chickpeas. Stir well to combine. Cook for 2-3 minutes.
Complete the Soup: Add cubed potatoes and shredded cooked chicken. Pour in chicken broth and season with salt and black pepper. Bring to a gentle boil, then reduce heat to medium-low. Simmer for 20-25 minutes, or until the potatoes and carrots are tender.
Serve: Taste and adjust seasoning as needed. Ladle the hot soup into bowls and serve with lime wedges on the side.