Warm a large, heavy skillet over high heat and lightly grease with oil. Reduce heat to medium. Season steak with salt and pepper and sear for 5 to 7 minutes per side, or until thermometer inserted into the thickest part of the steak reads 145°F (for medium rare). Remove from heat and set steak aside to rest. Wipe out skillet and turn off heat.

Heat broiler to high. Place poblano pepper on a small baking sheet under broiler, turning occasionally, for 4 minutes, or until blackened on all sides. Place in a paper bag, close, and let rest 5 minutes. Remove pepper and rub off blackened skin, remove stem and seeds and discard, and cut pepper into roughly ½-inch strips.

Heat oven to 400°F. Add 2 tablespoons corn oil to a medium skillet over medium heat. Add onion and sauté 30 seconds. Add poblano strips and mushrooms and cook for 2 minutes more, or until mushrooms are cooked through. Season with salt and pepper to taste.

Cut steak into ¼-inch-thick slices, add to skillet with vegetables, and toss to combine. Sprinkle cheese over dish and place in oven for 5 minutes, or until cheese is bubbling. While cheese is melting, heat tortillas in a large skillet over medium-low until softened and warmed through. Serve queso straight from the oven family style, spooning it out onto the tortillas.