These hearty tacos, piled high with braised pork and topped with a shower of thinly sliced cabbage and cilantro, are a love letter to the Mexican cooking traditions that shape California cuisine. Fried in pork fat after cooking low and slow, the pork gets extra crispy without being dry. Dried chiles bring a mild, sweet heat to the salsa; their slight bitterness cuts through rich, fatty pork.

Direction

1. Score fat cap on pork shoulder in a 1 1/2-inch diamond pattern, cutting just until tip of the knife reaches meat. Flip pork shoulder over; cut along bone (about 3 inches deep) to open up meat. Rub pork shoulder all over with 3 tablespoons salt. Place on a rimmed baking sheet, and cover tightly with plastic wrap. Refrigerate 8 to 24 hours.
2. Preheat oven to 375°F with oven rack in lower third of oven. Place pork shoulder, fat cap side up, in a large ovenproof Dutch oven. Add bay leaves and 6 cups water. Bring to a boil over medium-high. Cover and transfer Dutch oven to preheated oven. Roast until meat is fork-tender, 3 hours to 3 hours and 30 minutes, flipping pork shoulder after 2 hours. Let cool, covered, at room temperature 1 hour.
3. Meanwhile, increase oven temperature to broil with oven rack in middle of oven. Place onion, tomatoes (cut sides down), and garlic on a lightly greased (with lard) rimmed baking sheet. Broil until onion and tomatoes are lightly charred and garlic is softened, 8 to 10 minutes for garlic and 10 to 14 minutes for tomatoes and onion. Set aside until cool enough to handle, about 10 minutes. Peel garlic cloves. Reduce oven temperature to 250°F.
4. While tomato mixture broils, heat all dried chiles in a dry large cast-iron skillet over medium. Cook, turning occasionally, until chiles are fragrant and darkened in spots, 4 to 5 minutes. Transfer chiles to a small saucepan; add remaining 3 cups water, and bring to a boil over medium-high. Reduce heat to medium-low; cook, stirring occasionally, until chiles are softened, about 10 minutes. Drain, reserving chile cooking liquid.
5. Combine onion, tomatoes, garlic, chiles, vinegar, sugar, oregano, remaining 2 teaspoons salt, and 1 1/4 cups reserved chile cooking liquid in a blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, about 30 seconds, adding up to 1/2 cup additional chile cooking liquid, if needed, to thin salsa to pourable consistency. Season with salt to taste.
6. Remove pork shoulder from Dutch oven; discard braising liquid. Pull meat into bite-size pieces; discard bone and large pieces of fat. Heat 2 tablespoons lard in cast-iron skillet over medium-high. Add just enough pork (2 to 3 cups) to cover bottom of skillet in a single layer, and press lightly to flatten. Cook until crispy and lightly browned, 4 to 6 minutes, flipping meat halfway through cook time and seasoning both sides with salt to taste while cooking. Transfer pork to an ovenproof serving platter, and keep warm in 250°F oven. Repeat with remaining pork, adding more lard to skillet as needed. Serve with corn tortillas, shredded cabbage, cilantro leaves, lime wedges, and salsa.