On hot griddle toast the ancho and gaujillo chile and submerge in hot water. Let chiles sit for 20 minutes. Remove from water and puree in blender with a cup of warm water. Set aside.
In a deep Dutch oven, add the beef and ribs, water, onion, and garlic cloves. Bring to boil and cook for 1 hour. At this point add the bay leaves, thyme, chile puree, cumin, oregano, salt, and pepper simmer for 30 minutes. To make sauce, puree the garlic, vinegar, and chile powder in a blender.
Serve the stew in a big bowl with a sprinkle of onion and cilantro and a squeeze of lime on top. Serve with corn tortillas and some of the sauce on the side, as well.