1. 1. Begin by roasting the poblano peppers over an open flame or under the broiler until charred on all sides. Place the roasted peppers in a bowl, cover with plastic wrap, and let them steam for 10 minutes. Once cooled, peel, seed, and chop the peppers.

2. 2. In a large pot, melt the butter over medium heat. Add the chopped onion and minced garlic, and sauté until the onion is translucent and the garlic is fragrant.

3. 3. Pour in the chicken bone broth and bring the mixture to a simmer. Add the cubed chicken and cook until the chicken is fully cooked, about 10-12 minutes.

4. 4. Reduce the heat to low and stir in the cream cheese, allowing it to melt and create a smooth, creamy base for the soup.

5. 5. Gently fold in the chopped roasted poblano peppers, ensuring they are evenly distributed throughout the soup.

6. 6. Layer the cheddar or pepper jack cheese slices on top of the soup, allowing them to melt into the hot broth.

7. 7. Taste the soup and adjust the seasoning with salt and pepper as needed. Serve hot.