Slow Cooker Method: Place the chicken, green enchilada sauce, and chicken broth into a 6-quart slow cooker. Set the cooker to Low and let it cook for 6-8 hours. Once the chicken is done, remove and shred it, then return it to the pot. Add the Monterey Jack cheese, cream cheese, half and half, and salsa verde. Set the cooker to Warm and stir until the cheese has fully melted. Taste and adjust with salt and pepper. Serve with optional toppings such as avocado, cilantro, green onions, and sour cream.

Instant Pot Method: Place the chicken in the Instant Pot with 1 cup of chicken broth. Set the pot to High Pressure for 8 minutes. After cooking, quickly release the pressure and shred the chicken. Switch the pot to the Sauté setting. Add the remaining broth, shredded chicken, enchilada sauce, and salsa. Stir well and heat through. Then, mix in the cheeses, half and half, and salsa verde. Stir until smooth. Season with salt and pepper to your taste.

Stovetop Method: Simmer the chicken in a large pot with chicken broth until fully cooked and tender. Shred the chicken. Add the shredded chicken to the pot with the green enchilada sauce, half and half, Monterey Jack cheese, cream cheese, and salsa verde. Warm over low heat, stirring occasionally until the cheese has melted and the soup is hot. Adjust the seasoning with salt and pepper and serve with optional toppings like salsa, hot sauce, and sour cream.