BRAISE THE MEAT Preheat the oven to 325°. In a medium skillet, toast the ancho chiles over moderate heat, turning, until pliable and charred in spots, about 2 minutes; let cool slightly, then tear into pieces.
In a large roasting pan, toss the ancho and chipotle chiles with the celery, carrots, onion, garlic and bay leaves. In a large bowl, toss the short ribs with the oregano, cumin and 2 tablespoons of salt. Arrange the ribs over the vegetables in the roasting pan. Add 2 cups of water to the pan, cover tightly with foil and braise in the oven for about 3 1/2 hours, until the meat is very tender.
MAKE THE CHILE SAUCE Transfer the ribs to a baking sheet. Strain the braising liquid through a colander set over a heatproof bowl; skim off any fat. Discard the bay leaves and return the vegetables and chiles to the braising liquid. Working in batches, puree the vegetables and liquid in a blender until smooth. Season the sauce with salt and pepper.
GRILL Light a grill or preheat a grill pan. Working in batches if necessary, grill the ribs over high heat, turning occasionally, until charred and crisp, about 5 minutes total. Transfer to a platter and, using two forks, shred the meat; discard the bones. Serve the barbacoa in warm corn tortillas with the sauce, cilantro, chopped onion, lime wedges and Salsa Verde Cruda.