Roast Poblanos: Turn on the flame on your gas stove and place poblano peppers on the flame. Turn often until charred. OR in the oven: Place the poblano peppers on a sheet pan and drizzle with olive oil and season with salt and pepper. Toss to coat. Broil on high for 3-5 minutes, turning halfway, or until the skin is browned and blistered.
In a large dutch oven, heat oil on medium-high heat.
Add onion, garlic, and carrots. Sauté for 3-5 minutes, or until onion is translucent.
Chop the poblanos into small pieces then add the poblano peppers and the spices and stir for 1-2 minutes.
Once at a boil, turn down heat and add in chicken. Let simmer covered for 20-25 minutes until chicken is fully cooked through and no pink remains. Take soup off the heat.
Gently take the chicken out of the soup. Let cool, shred and set aside.
Using a liquid measuring cup, scoop 4 cups of soup into a high-speed blender. Blend until smooth and creamy. Add pureed soup and shredded chicken back into the soup and stir well.
Taste and adjust seasoning as needed.
Serve warm with desired toppings!
Instead of transferring 4 cups of soup to a blender, feel free to use an immersion blender in this step if desired! If using an immersion blender, make sure to leave some of the veggies whole, and avoid over-blending. The soup shouldn't be a pureed soup!
This soup isn't super spicy, but to avoid spice, scrape out seeds from any peppers!