Make the marinade. Toast the chiles a few pieces at a time in an ungreased skillet over medium heat, using a metal spatula to press them firmly against the hot surface until they release their aroma and change color slightly, then flip them over and press to toast the other side. Collect in a bowl, cover with hot tap water and let rehydrate until soft, 20 to 30 minutes. Place the garlic in a small microwave-safe dish, cover with water and microwave 1 minute; drain. Drain the chiles, reserving the soaking liquid, and place them in a blender jar along with the garlic, black pepper, cinnamon, chipotle(s), pineapple juice or pineapple, vinegar, agave syrup or one of its stand-ins and ½ cup of the soaking liquid. Blend until smooth, then press through a medium mesh sieve to remove unblended skins and stray seeds. (If you’re working with a high speed blender, there’s no need to strain). Taste and season with salt, usually a generous 1 ½ teaspoons.
Flavor and cook the meat. Mix the meat slices with half the marinade (store the rest of the marinade in the refrigerator for another round of Gringas). Heat a very large (12-inch) skillet over medium-high. Add the oil or lard and, when hot, lay in the meat in a single layer. Let cook undisturbed for a couple of minutes, until browning underneath, then turn the pieces over and let brown on the other side until fully cooked and tender, about 2 minutes. Remove the meat to a cutting board and cut into 1/4-inch strips (if they are longer than about 1 ½ inches, cut the strips in half). Sprinkle with salt.
Make the gringas. Heat a large skillet or griddle over medium. Lay on as many tortillas as comfortably fit, top each with a portion of cheese, spreading it on evenly, then cover with a portion of meat. Sprinkle with about a tablespoons of the raw onion, then top with another tortilla. When the tortilla is browned underneath, about 2 minutes, flip the whole assemblage and brown the other side. The cheese should be completely melted. As the gringas are ready, remove them to a cutting board, cut into quarters and serve right away with the salsa and a good sprinkle of queso añejo.