Step 1

Place chicken breasts, water, and onion in a multi-functional pressure cooker (such as Instant Pot®). Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 30 minutes. Allow 10 to 15 minutes for pressure to build.

Step 2

Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Drain off water. Shred chicken using 2 forks. Mix in green chiles.

Step 3

Combine chicken mixture with Monterey Jack cheese. Spoon some of the chicken filling into the middle of each tortilla and roll up tightly. Grease a 9x13-inch casserole dish; arrange filled tortillas in the dish.

Step 4

Preheat the oven to 350 degrees F (175 degrees C).

Step 5

Melt butter in a saucepan over medium heat. Stir in flour and cook for 1 minute. Add water, chicken stock concentrate, and cumin; whisk until smooth. Cook over medium heat until thick and bubbly, about 5 minutes. Stir in Greek yogurt, pepper Jack cheese, and Monterey Jack cheese. Do not boil, as yogurt may curdle.

Step 6

Pour sauce over enchiladas in the casserole dish.

Step 7

Bake in the preheated oven until cheeses melt, about 22 minutes. Broil on high until top browns, about 3 minutes.