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

Broil poblanos in the oven for 5 minutes or until the skin is blackened and blistered. Flip them over and broil for another 5 minutes until the skin is blackened and blistered on all sides.

Remove from the oven, loosely cover the baking sheet with aluminum foil or plastic wrap, and let sit for 5 minutes.

Pull and rub off as much of the loose skin on the peppers as possible. Transfer poblanos to a cutting board, slice open, discard the stems and seeds, and dice into small chunks.

Add the butter and oil to a large pot or Dutch oven over medium heat. When the butter has melted, add the onions and sauté for 5-7 minutes until soft and translucent.

Add the garlic and cumin and cook for 30-60 seconds until fragrant.

Add the flour and stir until the onions are evenly coated. Reduce the heat to low and cook for an additional 2 minutes, stirring occasionally.

Stir in the chicken broth and heavy cream. Continue stirring until the soup begins to thicken.

Slowly add the Monterey Jack and sharp cheddar cheese, stirring constantly until the cheese is fully melted and incorporated.

Raise the heat to medium-high and add the roasted and chopped poblano peppers. Bring the soup to a simmer, reduce heat to low, cover, and cook for 15 minutes.

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