Roast The Poblanos: Place the poblano peppers directly over an open flame on your gas stove or broil them in the oven until the skin is charred. Once roasted, let them cool, peel off the skin, remove the seeds, and chop the peppers.
Season And Cook The Chicken: Preheat the oven to 375°F (190°C). Season the chicken breasts with 1/2 teaspoon kosher salt and coarse black pepper. In a large oven-safe skillet, heat canola oil over medium-high heat. Sear the chicken until golden brown on both sides. Transfer the skillet to the oven and bake for about 25-30 minutes or until the chicken reaches an internal temperature of 165°F (74°C). Allow the chicken to cool, then shred the meat.
Prepare The Soup Base: In a large pot over medium heat, melt butter. Stir in the flour to create a roux. Gradually whisk in the chicken broth until smooth. Add the roasted poblano peppers, roasted corn, black beans, diced red bell peppers, shredded cheddar cheese, shredded pepper jack cheese, lime juice, ground cumin, and cayenne pepper. Stir well.
Simmer And Add Cream: Let the soup simmer for about 15 minutes to allow the flavors to meld. Stir in half and half or heavy cream, and continue to simmer for an additional 10 minutes.
Garnish And Serve: Before serving, garnish the soup with thinly sliced jalapeños. Ladle the soup into bowls, and get ready to indulge in a bowl of pure delight!