In a 6-quart slow cooker, combine the boneless, skinless chicken breasts or thighs with the green enchilada sauce and chicken broth. Set your slow cooker to low and let the mixture cook for 6 to 8 hours, until the chicken is tender and easily shreds with a fork.

After the chicken has cooked, carefully remove it from the slow cooker using tongs. Shred it into bite-sized pieces with two forks and return back to the pot.

Mix in the half and half or heavy cream, Monterey Jack cheese, cream cheese, and green salsa. Stir until the cheeses melt and create a creamy texture, about 5-7 minutes.

Taste and season with salt and pepper as per preference. Simmer on low for an additional 10 minutes.