Preheat your broiler to high. Place poblano peppers on a baking sheet. Broil for 5-7 minutes, turning occasionally with tongs, until the skin is charred and blistered all over. Alternatively, you can roast them in a 400°F (200°C) oven for 20-25 minutes, or char directly over a gas flame.

Transfer the charred poblanos to a bowl and cover tightly with plastic wrap or place them in a paper bag and seal. Let them steam for 10-15 minutes. This makes the skin easier to remove.

Once cooled enough to handle, peel off the skin, core the peppers, and remove the seeds. Dice the roasted poblano flesh and set aside.

Heat 1 tablespoon of olive oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the diced yellow onion and cook, stirring occasionally, until softened and translucent, about 5-7 minutes.

Add the minced garlic and jalapeño (if using) and cook for another 1-2 minutes until fragrant, being careful not to burn the garlic.

Stir in the ground cumin, smoked paprika, and dried oregano. Cook for 1 minute more, stirring constantly, until aromatic.

Pour in the chicken broth and diced tomatoes (undrained). Add the diced roasted poblanos. Bring the mixture to a gentle simmer, then reduce heat to low, cover, and let it cook for 15-20 minutes to allow the flavors to meld.

For a smoother soup, you can carefully transfer about 1-2 cups of the soup base to a blender (use caution with hot liquids) and blend until smooth, then return it to the pot. This is optional, if you prefer a chunkier soup.

Stir in the rinsed black beans, frozen corn kernels, and shredded cooked chicken. Continue to simmer for another 5-7 minutes, or until the chicken is heated through and the corn is tender.

Remove the pot from the heat. Stir in the heavy cream and fresh lime juice. Season generously with salt and freshly ground black pepper to taste. Adjust seasonings as needed.

Ladle the hot soup into bowls. Garnish each serving with chopped fresh cilantro, shredded Monterey Jack cheese, and tortilla strips or crushed tortilla chips.