Prepare the Pork: Cut the pork shoulder into 1-inch cubes and season with kosher salt. Set aside.
Soften the Chiles: Remove the stems (and seeds for milder heat) from the guajillo, ancho, and pasilla chiles. Place them in a bowl and cover with boiling water. Let steam for about 30 minutes until tender.
Make the Chile Purée: Blend the softened chiles with 1 cup soaking liquid, 1 cup chicken stock, garlic, onion, jalapeño, Chimayo chili powder, cumin, and oregano. Purée until smooth. Strain through a fine-mesh sieve for a smoother sauce, if desired.
Cook the Pork: Heat vegetable oil in a large Dutch oven or stockpot over medium heat. Brown the pork in batches.
Simmer the Pork: Add 4-5 cups chicken stock and the chile purée. Bring to a boil, then reduce heat to low, cover, and simmer for 1 hour or until the pork is tender and the sauce thickens. Stir in apple cider vinegar and season with salt if needed.
Shred and Cool: Let the pork rojo cool, then shred with forks and mix back into the sauce. Reserve 1 cup of the sauce for the masa. Cover and refrigerate overnight.