Clean and dry the poblano peppers, then roast them until the skin has blackened/charred and blistered. (You can do this by either placing the peppers on a foil-lined cookie sheet a few inches under the broiler set to high, flipping once. Or setting them over an open flame on a gas burner, turning on all sides. It will take about 10 minutes.)

Transfer peppers to a plastic bag and seal to trap in the steam. Let cool, then rub off as much of the skin as possible either with your fingers or a pairing knife. Cut off the stem, then slice in half to remove and discard the seeds. Very finely chop up the peppers and set aside (or transfer to a food processor and give them a few quick pulses.)

In a medium pot, warm the butter and olive oil over medium heat. Add in the onion and saute, stirring frequently, until softened, about 3 minutes. Add in the garlic and cumin and cook until fragrant, about 20 seconds. Stir in the chopped poblanos.

Pour in the chicken broth, salt, and pepper. Bring to a boil, then reduce heat to a very gentle simmer.

Stir in the cooked, chopped chicken.

Add in the cream cheese and 2 cups of the cheddar cheese; whisk until melted and smooth.

Divide into 6 bowls and sprinkle each with the remaining ¼ cup cheddar cheese and the pepper jack cheese. Set under the broiler until melted and golden (watch it carefully so it doesn't burn.)

Garnish with just a bit of fresh chopped cilantro and enjoy!