Cook the Chicken:
In a large pot or Dutch oven, add chicken, chicken broth, and enchilada sauce. Bring to a simmer and cook for 20–25 minutes, or until chicken is fully cooked and tender.
Shred the Chicken:
Remove chicken from the pot and shred with two forks. Return shredded chicken to the broth.
Add Creaminess:
Stir in cream cheese until melted and fully incorporated. Add half-and-half (or heavy cream) and salsa verde.
Cheese It Up:
Reduce heat to low and stir in shredded Monterey Jack cheese until smooth and creamy.
Season to Taste:
Add salt and pepper as needed. Simmer for another 5 minutes to let flavors blend.
Serve & Enjoy:
Ladle soup into bowls. Garnish with fresh cilantro, sliced jalapeños, or crushed tortilla chips if desired.