In your slow cooker or Instant Pot, place the boneless, skinless chicken breasts or thighs. Pour in the green enchilada sauce and chicken broth, ensuring the chicken is fully covered. For a slow cooker, set it on Low and cook for 6-8 hours until the chicken shreds easily with a fork. If using an Instant Pot, cook on high pressure for 8 minutes, followed by a quick release.

Once the chicken is cooked, carefully remove it from the pot and place it on a cutting board. Use two forks to shred the chicken into bite-sized pieces, and return it to the slow cooker or Instant Pot.

Stir in the softened cream cheese alongside the shredded Monterey Jack cheese, half and half, and green salsa in your slow cooker or Instant Pot. Mix well until the cheeses melt and combine into a creamy, rich broth.

Taste your soup and season with salt and pepper as desired. If needed, add a splash more chicken broth for consistency. Serve hot, garnished with your favorite toppings like avocado, cilantro, or a dollop of sour cream.