Fire up a grill or grill pan over medium-high heat. You should be able to hover your hand a few inches above the grill surface for 5 seconds or so, but not more, before you'll need to pull away. That's hot enough.
Toast the chiles on the fire for about 1 minute, turning once. A little char is good; burned is not.
Pull the stem end off of the chiles, shake out most of the seeds, and grind the chiles in a food processor.
Add the sugar, salt, and garlic to the ground chiles in the processor bowl. Pulse until well combined.
Massage the steak deeply with the ancho rub. Flap meat is quite cavernous, so use your thumbs and fingers to press the rub into all the cracks and crevasses.
Spray a clean grill rag with cooking spray. Rub into the grill grates until they glisten.
Place the lime on the grill, cut sides down, and char for about 2 to 3 minutes before removing from the grill. Set aside in a small bowl.
Grill the steak, about 4 minutes on each side for medium-rare. Don't tinker with it. Allow for some uneven charring.
Transfer the steak to a cutting board to rest for 5 minutes.
Cut on a sharp bias, with your knife nearly parallel to the board, in very thin slices.
Squeeze the grilled lime halves over the sliced beef. Serve.