First, place the chicken breasts and 1 cup of chicken broth into your Instant Pot. Set the pressure to high and set to Manual Cook for 8 minutes. (Remember, the Instant Pot will not begin cooking the chicken until it reaches full pressure.)
After the pressure cooker is done cooking, allow it to naturally release for 10 minutes. Once 10 minutes have passed, you can perform a quick release to remove the rest of the steam.
Next, open the lid to your Instant Pot and, carefully remove the chicken breasts, place them in a medium-sized bowl or onto a large cutting board. Shred the chicken and set aside.
Next, turn on the saute medium feature. Return the shredded chicken to the Instant Pot and add the remaining chicken broth, green enchilada sauce, and salsa. Heat the mixture for about 5 minutes, until it’s warmed throughout.
Finally, add the whole milk, Monterey jack cheese, and cream cheese to the pressure cooker. Stir the soup occasionally until the cheese is melted.
Serve warm with desired toppings!