Roast the poblano peppers until their skins are nicely charred. Pop them into a sealed bag for about 10 minutes to steam, then peel off the skin and chop them.

In a pot, heat a drizzle of olive oil over medium heat and sauté the chopped onion and minced garlic until softened, about 5 minutes.

Combine the chopped roasted peppers, diced tomatoes, chicken broth, ground cumin, and a pinch of salt and pepper. Bring to a gentle simmer.

Stir in the shredded chicken and simmer for another 10-15 minutes.

Stir in the shredded cheese until melted, keeping the heat low to avoid rubberiness.

Ladle the soup into bowls and sprinkle with fresh cilantro before serving warm.