Prepare the Chicken: In a small bowl, combine the salt, cayenne, cumin, chili powder, and black pepper. Generously coat both sides of the chicken breasts with this spice mixture.
Roast Vegetables and Chicken: In a large roasting pan, add the olive oil, sweet potato, onion, celery, carrot, garlic, jalapeño, and poblano. Pour in half of the water, and add the bay leaves and oregano. Place the seasoned chicken breasts on top of the vegetables.
Bake: Roast in a preheated oven at 375°F (190°C) for 1 hour, or until the chicken and vegetables have developed a nice color.
Shred Chicken: Remove the roasting pan from the oven and place it on the stovetop. Carefully remove the chicken breasts, shred them, and set aside.
Blend Soup Base: Ladle the roasted vegetables and liquids from the pan into a blender. Blend until smooth, starting on low and gradually increasing to medium speed, for approximately three minutes.
Simmer Soup: Return the blended soup base to the roasting pan. Add the shredded chicken and the remaining water. Bring the mixture to a boil, then reduce heat and simmer for 20 minutes, or until the soup has slightly reduced and thickened.
Serve: Turn off the heat and serve the chicken and tomatillo soup warm.
