Add the beef, onion and salt to a large pot and add water to cover. Bring to a boil, reduce heat to medium-low and simmer for 1 1/2 to 2 hours, or until meat is very tender. Remove the meat and reserve the stock for soup or other recipes. Shred the meat with your fingers when it is cool enough to handle.
Add the olive oil, vinegar, oregano, salt and pepper to a large bowl and whisk together. Add the tomatoes, sliced onion and chiles and toss together. Set a side for a few minutes to let the vegetables marinate.
Gently toss the shredded beef and avocados with the marinated vegetables and adjust seasoning. Spread on a serving platter and serve chilled or at room temperature with warm tortillas.
Salpicón can also be made with chicken (salpicón de pollo), seafood (salpicón de mariscos) or tuna (salpicón de atún).
Other possible additions: chopped lettuce, chopped cucumbers, olives, pickled jalapeños.
Garnish with lime wedges, cilantro and crumbled queso fresco if you like.
Substitute sour orange juice or lime juice for the vinegar for a more tropical flavor.