Strain the stock. Remove the oxtails and reserve. Discard the vegetables. Set the strained stock aside to cool. (You can do this a day or two ahead, and refrigerate the stock. It should congeal into a jelly, with any remaining fat easily removable from the surface.)
When you're ready to go to the consomme stage, rinse the stockpot and put the stock back into it over medium heat.
While waiting for the stock to boil, combine the ground round, the chopped carrot, onion, and celery. Flatten it out into a sort of gigantic hamburger patty. Float this on top of the stock. (It might sink, but the boiling will make it rise.) Pour the egg white over this raft, and break the eggshells atop that.
When the pot comes barely to a boil, punch a few holes in the raft so that the stock bubbles up and over the raft. Keep the stock at a very light boil for about two hours, punching the raft down every now and then. Add the salt and Tabasco in there somewhere.
While waiting, pick the lean meat from the oxtails and make small bundles of it, tied with a thin green onion or a chive. Set aside.
Remove the raft and anything else floating in the stock, which should now be clear or close to it. Carefully skim the fat from the top of the pot. Strain the soup through a very fine sieve or (better) double cheesecloth.
About a half hour before serving, bring the consomme to a simmer. Add the carrots and potatoes and cook until tender. Ten minutes after adding the carrots and potatoes, add the celery. Add salt and pepper to taste if necessary.
Place a bundle or two of the oxtail meat on a soup plate and ladle the broth with its vegetables around it.
