Set your oven's broiler to high. Place whole poblano peppers on a baking sheet and broil for 5-7 minutes per side, until the skins are blackened and blistered. Transfer to a bowl, cover with plastic wrap, and let steam for 10 minutes. Peel off the skins, remove stems and seeds, and roughly chop.

Heat olive oil in a large Dutch oven over medium-high heat. Add the chopped onion and cook until softened, about 5-6 minutes. Add the minced garlic and spices (chili powder, cumin, smoked paprika) and cook for 1 minute until fragrant.

Stir in the crushed tomatoes, chicken broth, and chopped roasted poblanos. Season with salt and pepper. Add the chicken breasts, bring to a boil, then reduce heat to a simmer. Cover and cook for 20-25 minutes, until the chicken is cooked through.

Remove the chicken and shred it using two forks. Return the shredded chicken to the pot and simmer uncovered for 10 more minutes to meld the flavors. Taste and adjust seasoning.

While the soup simmers, heat vegetable oil in a skillet over medium-high heat. Fry tortilla strips in batches until golden brown and crispy, about 1-2 minutes per side. Transfer to a paper towel-lined plate and salt immediately.

Ladle the hot soup into bowls. Garnish generously with crispy tortilla strips, diced onion, chopped cilantro, and sliced jalapenos. Serve with a lime wedge on the side.