Roast the poblano peppers over an open flame or beneath your broiler until the skin is blackened and blistered, which should take about 5-7 minutes. Place in a covered bowl for 10 minutes to steam.

In a large pot, heat 1-2 tablespoons of olive oil over medium heat for around 2 minutes. Add diced onion and sauté until translucent, about 5 minutes. Stir in minced garlic and ground cumin, cooking for an additional minute.

Add diced tomatoes with green chiles, corn, and drained black beans to the pot. Peel, seed, and dice roasted poblano peppers and add them as well. Stir and fold in shredded chicken and chicken broth. Bring to a simmer.

Reduce heat to low and mix in softened cream cheese until completely melted and creamy, about 5 minutes.

Season soup with salt and pepper, then stir in chopped fresh cilantro and add a squeeze of lime juice before serving.

Ladle the soup into bowls, garnishing with optional sliced jalapeños and lime wedges.