Preheat your oven to 450°F (232°C) and prepare a baking sheet. Slice the poblano peppers in half lengthwise, drizzle with olive oil, and arrange them cut-side down. Roast the peppers for 20 minutes, watching for the skins to char and blister. Once done, remove from the oven, cool slightly, then peel off the skins, chop, and set aside.

In a large stock pot, heat ¼ cup of unsalted butter over medium heat until melted. Add the diced onion and celery, cooking them for about 9-10 minutes until they become tender and aromatic. Incorporate the diced baby gold potatoes, stirring them in for another 2 minutes. Finally, add minced garlic, ground cumin, red pepper flakes, salt, and pepper, cooking for 1 additional minute.

Pour 5 cups of lower-sodium chicken broth into the stock pot, along with the chopped roasted poblano pieces. Stir well to combine all the ingredients. Increase the heat and bring the mixture to a gentle boil for about 2-3 minutes.

Add 1½ to 2 pounds of boneless skinless chicken breasts into the pot. Lower the heat to medium and cover the stock pot, letting the chicken simmer for 10 minutes until fully cooked. Remove the chicken from the pot and let it rest for a few minutes before chopping it into bite-sized pieces.

Using an immersion blender, blend the soup in the stock pot until you achieve your desired texture. Blend until smooth for a creamier soup; if you prefer some chunky bits, blend selectively.

Return the chopped chicken pieces to the blended soup. Stir in 1 cup of heavy cream to enrich the flavor. Let the soup simmer gently for another 5 minutes, stirring occasionally.

Carefully ladle the soup into bowls, garnishing with freshly minced cilantro. Consider optional toppings like crispy tortilla strips, creamy avocado slices, or cheese to enhance the dish.