Preheat your oven to 450°F (232°C). Halve the poblano peppers and arrange them, skin side up, on a baking sheet. Drizzle with olive oil and roast for about 20 minutes until nicely charred.

In a large stockpot over medium heat, melt the unsalted butter. Add chopped onions, diced celery, and cubed potatoes, sauté for 9 to 10 minutes until softened. Stir in minced garlic, cumin, and red pepper flakes for 1 minute.

Pour in the chicken broth and chopped roasted poblano peppers. Increase heat to high and bring to a gentle boil.

Add the diced chicken breasts and reduce heat to low. Simmer for about 10 minutes until chicken reaches 160°F (71°C). Remove chicken, let it rest, and chop into bite-sized pieces.

Using an immersion blender, puree the soup to the desired consistency, blending lightly for a chunkier texture.

Return the chopped chicken to the pot and stir in the heavy cream. Simmer gently for a few more minutes, adjusting seasoning with salt and pepper as needed.

Ladle the soup into bowls and garnish with fresh cilantro. Serve with toppings like avocado slices, shredded cheese, or tortilla strips.