Rinse and dry the poblano peppers, then roast them until the skin is charred and blistered.
After roasting, transfer the peppers to a plastic bag and seal it to trap in the steam. Let them cool, then rub off as much of the skin as you can.
Cut off the stems, slice the peppers in half, and remove the seeds. Finely chop the peppers and set aside.
In a medium pot, melt the butter and olive oil over medium heat. Add the diced onion and sauté until softened.
Add the minced garlic and cumin, cooking until fragrant. Stir in the chopped poblano peppers.
Pour in the chicken broth, salt, and pepper. Bring the mixture to a boil, then reduce the heat to a gentle simmer.
Mix in the cooked, chopped chicken. Add the cream cheese and 2 cups of the shredded cheddar cheese; whisk until melted and smooth.
Divide the soup into bowls, sprinkling each with the remaining cheddar cheese and the pepper jack cheese. Place under the broiler until the cheese is melted and golden.
Garnish with fresh chopped cilantro and enjoy!
