Before dunking into the mole, soften and partially dry out the corn tortillas. Heat up a skillet over a medium flame, place tortillas (one at a time) into the pan. Heat on each side for about 30 seconds.
Preheat the broiler.
Carefully place corn tortillas (one at a time) into the simmering red mole, submerging and saturating both sides. (Tortillas can disintegrate when in contact with moisture.) Fill a tortilla with a heap of the shredded beef and roll it up into a cigar shape. Place it on broiler proof dish, top with shredded cheese and broil until cheese bubbles. Repeat with more tortillas until the meat is no more. Serve the leftover mole on the side.