Start by setting your oven broiler to high and placing your whole poblano peppers on a sheet pan. Broil them until the skins are nicely charred and blistered, turning occasionally. This step is key for that signature smoky flavor.
Once roasted, place the peppers in a bowl and cover tightly with plastic wrap or foil. Let them steam for about 10 minutes to loosen the skin. Then peel off the charred skin, remove the seeds, and roughly chop them. You can pulse them in a blender for a smoother texture.
In your large saucepan, melt the butter over medium heat. Add the chopped onion and cook until soft and golden, about 5–6 minutes. Stir in the garlic, cumin, and chopped roasted poblanos. The kitchen will smell amazing right about now!
Pour in your chicken bone broth and season lightly with salt and pepper. Bring to a gentle boil. Add the cubed chicken and let it simmer for about 10–12 minutes, or until the chicken is fully cooked and tender. Keep the heat low so the broth stays rich and doesn’t boil off too quickly.
In a blender, add the cream cheese, shredded cheddar, and a ladle of the hot broth from your pot. Blend until creamy and smooth. Pour this mixture back into the pot with the soup and stir to combine. The soup will instantly turn rich and velvety.
Ladle the soup into oven-safe bowls, and top each with a slice of cheddar or pepper jack. Place under the broiler for 1–2 minutes until the cheese is melted and bubbly. Serve hot with your favorite toppings or side dishes.