Place your boneless skinless chicken breasts or thighs into your slow cooker or Instant Pot. Pour in the green enchilada sauce and chicken broth, ensuring the chicken is well coated. For a slow cooker, set it on low and cover, allowing it to cook for 6-8 hours; for the Instant Pot, seal the lid and set it to pressure cook on high for 8 minutes.

As the chicken cooks, it will absorb the flavors of the sauce and broth. For the slow cooker, let the mixture bubble gently until the chicken is tender. For the Instant Pot, once cooking time is complete, use the quick release method for steam.

Once the chicken is cooked, carefully remove it from the cooker and shred it into bite-sized pieces.

Return the shredded chicken to your slow cooker or Instant Pot. Add in the softened cream cheese, half and half, shredded Monterey Jack cheese, and green salsa. Stir thoroughly until the cream cheese melts with the other ingredients.

Continue stirring until all the cheeses are melted and the mixture is smooth and creamy. Allow the soup to heat through for about 5-10 minutes, adjusting seasoning with salt and pepper to taste.