With a sharp knife, clean the cactus paddles by trimming all the edges and scraping off the spines. Measure 1 tablespoon of the lard, oil or bacon drippings into a large (12-inch), heavy well-seasoned skillet (preferably cast-iron) or griddle and set over medium-high heat. When hot, add the cactus and cook until done, about 8 to 10 minutes. Slice into strips.
Generously salt both sides of each piece of meat. Wipe the skillet or griddle and return it to medium-high heat. Add the remaining 1 tablespoon lard, oil or bacon drippings. When very hot (it’ll just begin to smoke), lay in the meat in a single layer. If it doesn’t all fit comfortably, you’ll need to do this in 2 batches. Sear the meat on one side until brown (about 1 1/2 minutes), flip it over, and sear the other side. Meat for tacos a la plancha is generally cooked well done. Transfer to your cutting board; tent with foil if you are searing the meat in batches.
Chop the seared steak into 1/2-inch bits (most Mexican taqueros do this with cleavers) and scoop into a serving bowl—a warm one makes a big difference in keeping the filling warm. Set on the table along with the cactus and warm tortillas. Salsa and lime wedges will be a welcome addition for garnishing your tacos.