1.)  Place the meat in a pot with about 8 cups (2 liters) water and the half onion. Cover and boil gently until the meat is very soft, probably an hour and a half to two hours. (Alternate method: Use a slow cooker and 4 cups water; cook on high for 3 hours or so.)

2.) Remove meat from water. Remove and discard onion. Save broth for another use (such as soup-making).

Once meat has cooled enough, shred it, using your fingers to pull it apart into pieces the size you desire. Remove and discard any fatty or nerve tissue.

3.) Finely slice the whole onion. Leave as-is or rinse the slices briefly (in a strainer under running water) and drain well if you prefer a less-pronounced onion flavor.

Chop the tomatoes into “cubes” and the lettuce into short strips.

4.) Make the dressing by combining the olive oil, vinegar, lime juice, oregano, and salt in a bowl and whisking well OR in a jar with tight-fitting lid and shaking.

5. In a large salad bowl mix the shredded meat with the sliced onion and half the dressing. Add the chopped tomatoes and lettuce and toss well with salad forks or tongs, stirring in the rest of the dressing little by little as you go.

Slice the avocado and arrange the slices attractively on top of the salad.

Serve immediately. Provide corn tostadas or crackers and, if desired, pickled jalapeños or jalapeño carrots so that each person can add these to taste.