Place pork shoulder chunks in a large pot and cover with cold water. Bring to a boil, then reduce heat and simmer for 90 minutes until pork is fork-tender and reaches an internal temperature of at least 75°C.

While pork cooks, toast the guajillo and ancho chilies in a dry skillet over medium heat for 30 seconds per side until fragrant. Place in a bowl and cover with 1 cup hot water. Soak for 20 minutes until softened.

Prepare the pickled onions: combine sliced red onion, lime juice, white vinegar, sugar, and 1/2 teaspoon salt in a bowl. Toss well and refrigerate for at least 30 minutes, stirring occasionally.

Drain the softened chilies, reserving the soaking liquid. Add chilies, garlic, oregano, cumin, cloves, apple cider vinegar, salt, and pepper to a blender. Blend until smooth, adding reserved soaking liquid as needed to reach a thick paste consistency.

Once pork is cooked, drain and reserve 1/2 cup of the cooking liquid. Using two forks, shred the pork into fine strands.

Heat vegetable oil in a large skillet over medium-high heat. Add the shredded pork and fry for 5 minutes, stirring occasionally, until edges begin to crisp.

Pour the chili paste over the pork and stir well to coat. Add the reserved cooking liquid and continue cooking for 10-12 minutes, stirring frequently, until the paste is absorbed and the pork is deeply flavored and slightly caramelized.

Warm corn tortillas in a dry skillet or directly over a gas flame for 20 seconds per side.

Assemble tacos by placing chilorio on warm tortillas and topping with drained pickled red onions and fresh cilantro. Serve immediately with lime wedges.