Place the beef, water and a big pinch of salt in a large saucepan and bring to a boil over medium heat. Reduce heat to low, cover and simmer for 1 to 1 1/2 hours, or until the beef is very tender.
Remove the beef to a bowl, reserving the broth, and set aside to cool
When cool enough to handle, shred the beef with your fingers and set aside.
While the beef is simmering, place the onion, tomatoes, tomatillos and chiles in a food processor or blender and puree, adding a little water if necessary.
Heat the oil in a large pot over medium flame. Add the onion-tomato puree and simmer until the puree is cooked down and darkens somewhat in color, about 10 minutes. Do not burn.
Add the shredded beef and about 3 cups of the broth to the onion-tomato puree and season with salt and pepper. Simmer for about 15 minutes.
Stir in the potatoes, onions and a little more broth or water if necessary Simmer until the potatoes and carrots are cooked through, about 15-20 minutes.
Stir in the breadcrumbs to thicken the sauce.
Then stir in the chopped cilantro, adjust seasoning and serve hot with corn tortillas or rice.