Season the chicken. Pat chicken dry and sprinkle both sides with salt, pepper, cumin, garlic powder, onion powder, and smoked paprika.
Load the crockpot. Add chicken to the slow cooker. Pour in the green chiles, green chile enchilada sauce (or tomatillo salsa), and chicken broth.
Cook low and slow. Cover and cook on Low for 4–6 hours or on High for 2.5–3.5 hours, until the chicken is very tender.
Shred the chicken. Transfer chicken to a board and shred with two forks.
Return the shredded meat and any juices back to the crockpot.
Make it creamy. Add the cream cheese and heavy cream. Stir until the cream cheese melts and the sauce turns smooth and thick. If needed, cover and let it warm for 10–15 minutes to fully blend.
Add cheese and lime. Stir in the shredded Monterey Jack and fresh lime juice.
Taste and adjust salt and pepper.
Serve. Spoon over cauliflower rice or into lettuce cups. Top with cilantro and your favorite garnishes.