In a large, heavy-bottomed saucepan, combine the onions, tomatoes, and oil and cook over medium heat, covered, for 1 hour. Remove from heat and toss with the vinegar, salt, and pepper, to taste.
In a large, heavy-bottomed saucepan, combine the onions, Place the beef, bones, tongue, chicken pieces, onion, carrot, and celery in a large soup pot, cover with the water and bring almost to a boil, very slowly. Reduce the heat to simmer before the mixture boils, and allow to cook for 4 hours, skimming off the foam and any excess fat that rises to the surface. After 4 hours, remove from heat, strain the liquid twice, first through a conical sieve and second through cheesecloth, and allow to cool. Refrigerate stock in small containers for up to a week or freeze for up to a month.
Place the tongue, beef brisket, and beef cheeks in a large soup pot, cover with cold brodo, add the vinegar, and bring to a boil. Lower heat to a high simmer and cook for 45 minutes. Add the sausages and the capon and bring to a boil, lower the heat to a high simmer, and cook covered for 30 minutes, replenishing with water as necessary to keep all meat covered.
To make the salsa verde, place the parsley, anchovies, capers, hard-boiled egg, cornichons, white wine vinegar, salt, and pepper in the food processor and blend until smooth, about 1 minute.
Remove the meat from the broth and serve some of the broth, the salsa verde, and friggone.