Place the cubed meat in a dutch oven, along with the bay leaves, onion, carrot, salt and peppercorns. Add enough water to cover and bring to a simmer over medium-high heat. Reduce heat to medium, cover partially, and simmer for 50 minutes to 1 hour, until the meat is tender enough to pull apart with a fork.
Place a strainer or a colander over a bowl and drain the meat. Reserve 1½ cups of the broth. Once the meat has cooled enough to handle, pull it apart shredding into thin pieces. Drain and dry the casserole dish.
Guajillo Sauce
Place casserole over medium heat. Once hot, toast the guajillo chiles turning often with a pair of tongs, until toasted, about 1 minute. Incorporate the tomatillos, garlic and cover with water. Bring to a boil over high heat. Reduce heat to medium and simmer until the tomatillos are thoroughly cooked and soft and the guajillos have rehydrated, about 12 minutes. Remove from the heat.
Using a slotted spoon, transfer the tomatillos, garlic and chiles to a blender along with 1 teaspoon salt, and puree until completely smooth. Drain and dry the casserole dish.
Heat the oil in the casserole over medium heat. When it is hot, add the chopped white onion, and cook until tender and the edges have begun to brown, about 5 minutes. Add the pureed tomatillo mixture, being careful and using the lid as a shield, as it will splatter.
Stir in the shredded meat and the reserved 1½ cups broth. Cover partially and simmer for 20 minutes more, stirring occasionally, until the sauce has thickened. Taste for salt and add more if needed.
Serve hot and if desired, with warm corn tortillas on the side.