Scoop the beef into a medium saucepan, cover it generously with water, add 2 teaspoons salt and set over high heat. When the water comes to a boil, reduce the heat to medium-low. Skim off the grayish foam that rises during the first few minutes of simmering. Partially cover and simmer until the meat is fall-apart tender, about 1 hour and 15 minutes.
With a slotted spoon, remove the meat to a plate to cool. Scoop the potatoes into the meat broth (if there isn't enough to cover the potatoes, add water) and simmer over medium heat until tender, about 15 minutes.
Use the slotted spoon to scoop the potatoes into a medium bowl, sprinkle with vinegar. Break the up the meat into coarse shreds and stir it into the potatoes, along with the chipotles, onion and olive oil. Let cool completely, then taste and season with salt if you think necessary. Cover and refrigerate until you're ready to serve.
Just before serving, scoop the mixture into a wide serving bowl and mix in the avocado.