Trim excess fat from the Pork Shoulder and cut into 2–3 inch chunks; pat dry and season generously with Kosher Salt, Black Pepper, Ground Cumin, and Mexican Oregano.
Heat about 2–3 tablespoons of Lard in a large Dutch oven or heavy pot over medium-high heat. Working in batches so you don’t crowd the pan, brown the pork on all sides until richly caramelized, then transfer pieces to a plate.
Reduce heat to medium and add the chopped White Onion and minced Garlic to the pot; cook, stirring, until softened and fragrant, about 3–4 minutes.
Return the browned pork to the pot and add the juice and the zest or halved peel of the Orange, the Bay Leaf, and enough Water to come about two-thirds up the sides of the meat.
Bring to a gentle simmer, cover, and braise on low heat (or in a 300°F/150°C oven) until the pork is fork-tender and easily shreds, about 2 to 3 hours.
Carefully remove the pork and set aside to cool slightly; skim fat from the braising liquid if desired, then simmer the liquid until reduced and slightly syrupy to concentrate flavor. Shred the pork with two forks and return it to the reduced liquid to soak up flavor.
For crisped carnitas, spread the shredded pork on a rimmed baking sheet and broil a few minutes until edges are crisped, or heat a skillet with a little Lard and pan-fry handfuls of the shredded meat until golden and crunchy in spots.
Warm the Corn Tortilla on a dry skillet until pliable and lightly charred. Fill each tortilla with the crisped carnitas, a sprinkle of diced White Onion, chopped Cilantro, a squeeze of Lime, and a spoonful of Salsa Roja.
Serve immediately, offering extra lime and salsa at the table for guests to customize.
