Roast poblanos over an open flame until charred on all sides (do not let them turn to ash). Transfer to a clean plastic bag and seal. Let them steam for at least 10 minutes. Remove from bag and scrape off charred skin with knife. Remove seeds and veins and slice into strips.

Heat oil in a large skillet over medium heat. Add onion and garlic. Cook until translucent, about 3 minutes.

Add poblano strips and corn. Cook for 12 minutes, stirring frequently.

Decrease heat to low and stir in cream. Season with salt and pepper. Simmer for 5 minutes.

Add cheese. Cover and remove from heat. Let cheese soften for 5 minutes.

Serve with warm corn tortillas.