Place meat in a large saucepan. Add water, peppercorns, ¼ onion and salt to taste. Bring to a boil; reduce heat. Cover and simmer until meat is very tender, about 1-1/2 hours. Cool meat in broth. Drain, reserving 1/3 cup broth. Shred meat with 2 forks. Set aside.

Mash garlic with ¼ teaspoon salt to make a paste. Heat oil in a large skillet. Add chopped onion and garlic paste. Cook until onion is tender. Cut chile into short strips. Add chile strips and tomatoes to cooked onion. Cook 3 to 4 minutes. Add meat, cumin and freshly ground pepper to taste. Cook and stir until meat is heated through. Stir in reserved broth. Taste and add salt if needed. Keep warm.

Preheat oven to 350°F (175°C). Wrap tortillas in foil and place in oven until softened, about 15 minutes.

Prepare salsa if making fresh. Mash avocado in a small bowl. Stir in lime juice and salt to taste. Beat until smooth. Place avocado mixture, onion, cilantro and salsa in separate bowls and set aside.

For each taco, place spoonful of Machaca on a warm tortilla. Top with avocado mixture, onion, cilantro and salsa to taste. Fold tortilla around filling. Serve immediately.