In a large skillet over a medium flame, heat 1 tablespoon of the vegetable oil. Sprinkle the steak with salt and pepper, and cook in the skillet for about 5 minutes per side for medium-rare. Remove from skillet and let rest for 5 minutes.
Combine the radishes, scallions, jalapeno, lime juice, and last tablespoon of oil in a medium bowl. Chop half of the cilantro and fold it into the radish salsa. Season to taste with salt and pepper.
Slice the steak into strips, and serve on warm tortillas with the radish salsa, cheese, and the remaining cilantro.