Roast the poblano peppers over an open flame or under a broiler until their skins are blackened and blistered, about 5–10 minutes. Place them in a bowl, cover with plastic wrap, and let them steam for 10 minutes to loosen the skin.

In a large pot, heat 2 tablespoons of olive oil over medium heat. Add diced onion and sauté until translucent, roughly 5 minutes. Add minced garlic and cumin, cooking for another minute until fragrant.

Stir in canned diced tomatoes with green chiles, corn, and drained black beans. Dice the roasted poblano peppers, remove skins and seeds, and add them to the mixture. Fold in the shredded chicken and pour in the chicken broth, bringing to a gentle simmer for 10 minutes.

Reduce the heat and add softened cream cheese to the pot, stirring continuously until it melts completely and forms a creamy consistency, about 10-15 minutes.

Season with salt and pepper. Just before serving, add chopped cilantro and a squeeze of lime.

Ladle the hot soup into bowls and serve immediately. Garnish with optional jalapeño slices and lime wedges.