Preheat your oven to 425°F (220°C). Place the poblano peppers on a baking sheet and roast them for about 15–20 minutes until nicely charred. Remove from the oven, cool, peel, deseed, and chop.
In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until softened. Then add minced garlic and sauté for another minute until fragrant.
Add the chicken breasts into the pot and season with salt, pepper, cumin, chili powder, and smoked paprika. Sear each side for about 3–4 minutes.
Pour in the chicken broth along with diced tomatoes, chopped roasted poblanos, corn kernels, and black beans. Stir and bring to a gentle boil.
Lower the heat and let the soup simmer for about 20 minutes until the chicken is cooked through.
Remove the cooked chicken from the pot and shred it using two forks. Return the shredded chicken back into the pot.
Add heavy cream into the pot and allow it to heat through for several minutes.
Taste and adjust seasoning as necessary by adding more salt, pepper, or spices.
Cut corn tortillas into strips and pan-fry or bake until crispy for garnishing.