Line a baking sheet with aluminum foil and place the poblano peppers on it. Set the oven rack underneath the broiler and turn the broiler on high.

Broil the poblanos for 5 minutes or until the skin is blackened. Flip and broil for another 5 minutes.

Remove from the oven, cover loosely with foil or plastic wrap to steam, and let sit for 5 minutes.

Rub off as much of the loose skin as possible from the peppers.

Slice open the poblanos, discard stems and seeds, and dice into small chunks.

In a large pot, melt butter and add olive oil over medium heat. Sauté the onions for 5-7 minutes until soft.

Add garlic and cumin, cooking for 30-60 seconds until fragrant.

Stir in flour until onions are coated. Cook for 2 additional minutes on low heat.

Add chicken broth and heavy cream, stirring until the soup thickens. Slowly add the cheeses, stirring until melted.

Add the roasted poblano peppers, bring to a simmer, reduce heat to low, cover, and cook for 15 minutes.

Serve in bowls topped with more cheese or toasted panko breadcrumbs if desired.