Prep the chicken: If using raw chicken, season lightly with salt and pepper. Poach in simmering broth for 12–15 minutes until cooked through, then shred.
If using rotisserie, just shred and set aside.
Sauté aromatics: Heat oil in a large pot over medium heat. Add onion and jalapeño. Cook 4–5 minutes until softened.
Stir in garlic and cook 30 seconds until fragrant.
Add spices and chiles: Stir in cumin, chili powder, oregano, and smoked paprika. Toast 30–60 seconds. Add diced green chiles and mix well.
Build the base: Pour in chicken broth.
Add riced cauliflower or diced zucchini if using. Bring to a gentle simmer for 8–10 minutes to soften veggies and marry flavors.
Make it creamy: Reduce heat to low. Add cream cheese in small cubes, whisking until fully melted and smooth.
Pour in heavy cream and stir until combined.
Add chicken: Stir in shredded chicken. Simmer on low 5–10 minutes to warm through and thicken slightly. Do not boil after adding dairy.
Finish: Stir in lime juice and cilantro.
Taste and adjust salt and pepper. Add more broth to thin or simmer a few extra minutes to thicken.
Serve: Ladle into bowls and top with avocado, shredded cheese, or a dollop of sour cream if you like.