Sauté the aromatics: Warm 1–2 tablespoons oil in a large pot over medium heat. Add onion, green bell pepper, and jalapeño.
Cook 4–5 minutes until softened. Stir in garlic and cook 30 seconds, just until fragrant.
Bloom the spices: Add chili powder (2 teaspoons), cumin (2 teaspoons), smoked paprika (1 teaspoon), coriander (1/2 teaspoon, if using), oregano (1 teaspoon), 1 teaspoon salt, and 1/2 teaspoon black pepper. Stir 30–60 seconds to wake up the spices.
Build the base: Stir in 1–2 tablespoons tomato paste, then add crushed tomatoes (about 14–15 ounces), green chiles (1 small can), and 4 cups chicken broth.
Bring to a gentle simmer.
Add the chicken: Nestle 1.5–2 pounds of chicken breasts or thighs into the pot. Simmer gently, partially covered, for 15–20 minutes (breasts) or 20–25 minutes (thighs) until cooked through.
Shred and return: Transfer chicken to a board and shred with two forks. Return the chicken to the pot and lower the heat.
Make it creamy: Cube 4–6 ounces of cream cheese and whisk it into the soup over low heat until fully melted and smooth.
If you’d like it richer, add 1/4–1/2 cup heavy cream.
Add the cheese: Stir in 1 cup shredded cheese until melted. Taste and adjust salt, pepper, and spices. For more heat, add a pinch of cayenne or a splash of hot sauce.
Garnish and serve: Ladle into bowls and top with cilantro, a squeeze of lime, avocado, extra cheese, or a sprinkle of crushed pork rinds for crunch.