Prepare the Ingredients: Begin by roasting the green chiles. You can roast them directly over a gas stove flame, turning frequently until the skins are evenly charred. Alternatively, preheat your oven to 450°F (230°C), place the chiles on a baking sheet, and roast for 20-25 minutes, turning occasionally. Once charred, place the chiles in a covered bowl for about 10 minutes to let the steam loosen the skins. Peel off the skins, remove the seeds, and chop the chiles into small pieces.

Sauté the Aromatics: In a large pot, melt the butter over medium heat. Add the minced garlic and chopped onion, and sauté until the onion becomes translucent and fragrant, about 5 minutes.

Add the Chicken and Chiles: Stir in the shredded chicken breast and chopped roasted green chiles. Cook for another 2-3 minutes, allowing the flavors to meld together.

Season the Soup: Season the mixture with salt, black pepper, and ground cumin. Stir well to ensure the seasonings are evenly distributed.

Incorporate the Broth: Pour in the chicken broth and bring the soup to a gentle simmer. Reduce the heat to low and let it cook for about 15 minutes, allowing the flavors to develop.

Add the Greek Yogurt: Slowly stir in the plain Greek yogurt, making sure it’s fully incorporated into the soup. This will give the soup a creamy texture without making it too heavy.

Thicken the Soup (Optional): If you prefer a thicker soup, mix the cornstarch with water to create a slurry. Gradually add this mixture to the soup, stirring continuously until the soup thickens to your desired consistency.

Serve: Ladle the soup into bowls and serve hot. You can garnish with additional toppings like chopped cilantro, a dollop of extra Greek yogurt, or a sprinkle of cheese if desired.