Put the short ribs in a large heavy pot. Season with 3 teaspoons salt and cover with water by about 1 inch. Bring to a boil over medium heat, skimming any foam from the surface. Reduce the heat to low and simmer until the meat is tender, 2 hours, 30 minutes to 3 hours. Transfer the short ribs to a cutting board with a slotted spoon and let cool slightly, then shred the meat from the bone. Skim the fat off the broth in the pot; reserve the broth.
Meanwhile, soak the dried chiles in warm water until soft, about 30 minutes. Drain and transfer to a blender; add the tomatoes, onion, garlic, peppercorns, achiote paste and cumin and process until smooth, adding water if necessary.
Mix about 1 cup reserved broth into the chile puree, then pour the puree through a fine-mesh sieve into the pot of broth. Bring to a boil, then reduce to a simmer and cook until thickened, about 30 minutes. Add the shredded meat and simmer 10 more minutes. Season with salt and pepper.
Use tongs to divide the meat among the tortillas. Top with pickled onions; serve with the remaining cooking liquid and lime wedges.
Pickled Red Onions
Mix 1 thinly sliced large red onion, 3/4 cup each white vinegar and water, 6 tablespoons sugar and 1/2 teaspoon each crumbled oregano and salt in a large resealable plastic bag; seal and shake, then refrigerate at least 24 hours.
Photograph by Andrew McCaul
Recipe courtesy Marcela Valladolid for Food Network Magazine