Simmer the beef. Measure about 1 quart water into a large (4-quart) saucepan. Set over medium-high heat and add 1 teaspoon salt. When the water comes to the boil, add the beef (there should be enough water to submerge the beef). When the water returns to a simmer, reduce the heat to keep it just barely simmering—not boiling. If you want clear broth to use in another preparation, skim the foam that rises during the next few minutes. Add half the onion, and the 2 halved garlic cloves, along with the bay leaves and oregano. Gently simmer, partially covered, until thoroughly tender, about 1 1/2 hour. For the juiciest shredded beef, let the meat cool in the broth.
Finish the filling. Coarsely shred the beef and dry on paper towels. Puree the tomatoes in a blender or food processor. In a large (10-inch) skillet, heat the lard or oil over medium-high. When hot, add the remaining half onion and cook, stirring regularly, until lightly brown, about 5 minutes. Add the beef and cook, stirring frequently, until the meat is lightly browned (the onion will continue to darken), 4 or 5 minutes more. Add the 2 finely chopped garlic cloves and stir for a minute, then add tomato and chile. Stir regularly until the tomato has been absorbed and the mixture still looks a little juicy—not saucy, 7 to 8 minutes. Taste and season with salt, usually about 1/2 teaspoon, and it’s ready to use.
A note about beef. At our restaurant, we often have trimmings from the whole beef rib sections that we cut into rib eye steaks. I’m not going to suggest you buy rib eye for this preparation, but it sure is succulent and rich-tasting. In my opinion, the most affordable option for a really good shredded beef is chuck, but short rib is meatier tasting and has even better texture. You can use a piece of flank or brisket, but both will yield a more textured, less luscious shredded beef.
A note about tomatoes. If using fresh tomatoes, start with about 1 ½ pounds. Roast and peel them: that’ll give you the 14 to 16 ounces you need for this recipe.