In a large pot or Dutch oven, add beef, bay leaves, 1 tablespoon salt, and enough cold water to just cover the meat and bring to a boil. Cover and reduce heat to medium; simmer until beef is very tender, 1 ½ to 2 ½ hours.

Use a spider skimmer or large slotted spoon to transfer meat to a large cutting board.(Reserve the beef broth to use in other recipes.) Let sit until cool enough to handle, about 15 minutes. Use a meat mallet or potato masher to flatten beef and loosen its fibers, forming a mix of fine shreds and larger pieces (see notes). Remove any large stringy fibrous pieces and gristle and discard.

In a large bowl, whisk to combine 1 tablespoon lime juice, garlic, 1 teaspoon salt, black pepper, and cumin. Add shredded beef to bowl, toss to combine, and use hands to further shred into bite-size pieces; set aside.

In a large skillet, heat 1 tablespoon oil over medium heat until shimmering. Add onion and remaining ¼ teaspoon salt, and cook until onion begins to soften and become translucent, 5 to 7 minutes. Transfer onion to a platter and cover with foil to keep warm. Do not wipe out skillet.

In now-empty skillet, add remaining 3 tablespoons oil and heat over medium-high heat until shimmering. Working in batches to prevent crowding the pan, spread beef in a thin, even layer. Cook uninterupted until bottom is crisped, 3 to 4 minutes, then us a spatula to flip beef, and continue cooking until beef is browned and crispy on both sides, 2 to 3 minutes. Transfer cooked beef to platter with onions. Repeat with remaining beef, adding 1 tablespoon oil if the pan is too dry.

Return onions and beef to pan together and cook over medium heat, stirring to combine, until heated through, about 1 minute. Turn off heat and mix in remaining 1 tablespoon lime juice. Serve immediately with lime wedgesand black beans and rice, if desired.