Combine the tomato paste, tomatoes, potato, zucchini, onion, jalapeno, garlic, oregano, cumin, cilantro and hominy in a 6-quart slow cooker. Add the crushed tortilla chips, the chicken broth and 1 teaspoon salt. Cover and cook on low, 7 1/2 hours. Add the chicken and cook 30 more minutes.
Combine the cheese and milk in a medium microwave-safe bowl; microwave, whisking occasionally, until melted and smooth, 2 to 3 minutes. Serve the soup topped with tortilla chips, the cheese sauce and sliced jalapeno.