Preheat the oven and roast the poblano peppers until their skins are blistered and blackened in spots, about 10-15 minutes. Once roasted, place them in a bowl covered with a towel to steam, making their skins easier to peel.
While the peppers cool, season the chicken breasts with salt, pepper, and a teaspoon of cumin. In a large pot, heat a tablespoon of oil over medium heat and brown the chicken for 5-7 minutes until golden on both sides. Remove and set aside.
In the same pot, add diced onion and minced garlic, cooking until fragrant and translucent, about 3-4 minutes. Chop the cooled roasted poblano peppers, removing their stems and skins as needed, then add them to the pot and cook for another 2 minutes.
Return the chicken to the pot, add chicken broth, and bring to a simmer. Cover and cook for 15 minutes, allowing the flavors to meld. Once cooked, shred the chicken directly in the broth using two forks.
While the soup simmers, slice corn tortillas into thin strips and fry them in a skillet with a bit of oil over medium heat until crispy and golden brown, about 2-3 minutes per batch. Drain on paper towels.
Adjust the soup’s seasoning with salt and pepper to taste. Ladle the hot soup into bowls, topping each with shredded cheese and a handful of crispy tortilla strips for added texture and flavor.
Optionally, garnish with fresh herbs or a squeeze of lime for extra brightness before serving. Enjoy your warm, smoky chicken and roasted pepper soup with crunchy tortillas!