Combine smoked paprika, garlic powder, onion powder, ground cumin, salt, and black pepper in a bowl to create the dry rub.
Pat the pork shoulder or butt dry with paper towels then generously coat all sides of it evenly using flour. Make sure there are no wet spots remaining as they will steam during cooking instead of frying, which creates an undesirable texture and can lead to bacterial growth.
In a large skillet or Dutch oven over medium-high heat add oil (about 1 tablespoon for pork shoulder) then sear the seasoned meat on all sides until it has nice brown color. This should take around 5 minutes per side, but keep an eye as times may vary based upon your stove and how thickly you coat with flour.
Once done browning remove from pan to rest for a few moments while preparing the remaining ingredients (you can place it on plates or in foil-lined pans).
Reduce heat down if necessary so that there isn't too much smoke, and add enough lard until you have about 1/4 to 1/2 inches of oil. This is deep frying! Be very careful not to get the fat itself on fire (it can happen quickly). Using a long-handled utensil carefully submerge pork into hot grease, ensuring that it's completely covered.
Fry until meat reaches an internal temperature of 190 degrees Fahrenheit and exudes its juices easily when pricked with tongs (this should take about 25-35 minutes but monitor closely as times may vary). Drain excess oil on a wire rack or paper towels.
Allow meat time for it to rest, this helps the flavors come together and keeps moisture in during carving. Slice against grain into strips (about 1/4-inch thick), serve with your choice of warm tortillas along side salsa verde or pico de gallo.
Optional: Wrap individual tacos tightly so that they don't fall apart when being eaten. Garnish as desired.