Line a baking sheet with aluminum foil and place the poblano peppers on top. Set your 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, cover the baking sheet loosely with aluminum foil or plastic wrap, and let the peppers steam for 5 minutes.

Rub off as much of the loose skin on the poblanos as possible. Slice open, discard the stems and seeds, and dice into small chunks.

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

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

Stir in the flour, mixing until the onions are evenly coated. Reduce 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 thickens, then slowly add the Monterey Jack and sharp cheddar cheese, stirring constantly until melted and incorporated.

Raise the heat to medium-high and add in 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.