Place meat, onion, garlic, bay leaves and salt into a large stockpot. Cover with water and bring to a boil. Reduce the heat to medium-low and simmer until the meat is tender (read note 1).
Once the meat is cooked, allow it to cool down a bit then shred it using 2 forks or place it on a large bowl and use an electric mixer to shred it quickly (read note 2).
Place the shreded meat into a large bowl and set aside.
Make the dressing
Place all ingredients on a jar with a lid, use only a little salt and pepper (you can adjust later) and close the lid. Shake until everything is combined. Set aside.
Make the salad
Add lettuce, tomatoes, onions, radish, and jalapenos to the bowl with meat. Drizzle with the dressing and toss everything until fully coated.
Add avocado and gently mix to infuse with flavors.
Adjust with salt and pepper if needed. Then allow the salad to rest for 15 minutes before serving.
If you using a regular stockpot and cooking the meat on the stove, it can take up to 3 hours to have it fully cooked. Other options for cooking the meat might include the crockpot (overnight, at low for 8 hours), the instant pot (about 45 minutes) or also a pressure cooker.
Shred your meat when is still a bit hot, it would be easier than cooled meat.
Make sure to add the dressing about 15 to 20 minutes before serving. It is an ideal time frame to infuse the flavors.