Preheat your broiler to high. Place poblano peppers on a baking sheet and broil, turning occasionally, until the skin is charred and blistered, about 8-10 minutes.

Remove the peppers from the oven and transfer them to a bowl. Cover with plastic wrap and let them steam for 10 minutes. This will make the skin easier to peel.

While the peppers are steaming, heat olive oil in a large pot over medium heat. Add diced onions and minced garlic, and sauté until softened, about 5 minutes.

Stir in ground cumin and coriander, and cook for an additional 1-2 minutes until fragrant.

Once the poblano peppers have steamed, remove them from the bowl and peel off the skin. Remove the stem and seeds, then roughly chop the peppers.

Transfer the chopped poblano peppers to a blender along with 1 cup of chicken broth. Blend until smooth.

Add the blended poblano mixture to the pot with the onions and garlic. Stir in the remaining chicken broth, diced chicken breasts, diced tomatoes, and black beans.

Season with salt and pepper to taste. Bring the soup to a simmer and cook for 20-25 minutes, or until the chicken is cooked through and tender.

Stir in fresh lime juice to brighten the flavors of the soup. Taste and adjust seasoning as needed.

Ladle the soup into bowls and garnish with fresh cilantro. Serve hot with a dollop of sour cream, if desired.