In a medium pot or Dutch oven, melt the butter over medium heat. Add the chopped onions, poblano pepper, and half of the seasoning blend. Cook for 5-6 minutes until the vegetables are tender and lightly browned.
Stir in the shredded chicken, black beans, frozen corn, chicken broth, and the remaining seasoning. Turn the heat to medium-high and bring the soup to a simmer. Let it simmer uncovered for 15 minutes to allow the flavors to meld together.
Stir in the heavy cream and shredded cheese, stirring continuously until the cheese is melted and the soup is creamy. Bring the soup back to a gentle simmer.
Allow the soup to simmer for an additional 15 minutes, letting the flavors develop. Stir in the fresh lime juice and season with salt and pepper to taste.
Divide the hot soup between bowls and garnish with freshly chopped cilantro. Add your favorite toppings, such as more shredded cheese, sour cream, or tortilla strips.