How to Make It
In a large pot, combine the celery, yellow onion, garlic, leek, thyme, bay leaves, peppercorns and 1 tablespoon of salt. Add the veal, wine and 4 cups of water and bring to a boil. Cover partially and simmer over moderately low heat, skimming occasionally, until the veal is tender, about 2 hours. Using a slotted spoon, transfer the veal to a medium bowl. Strain the cooking liquid into a large heatproof measuring cup; if you don’t have at least 3 cups, add water to make 3 cups. Discard the solids; wipe out the pot. Return the liquid to the pot.
Meanwhile, cook the egg noodles in a medium pot of boiling water until al dente, 7 to 9 minutes. Drain the noodles, then run them under cold water to cool; drain again.
Bring the veal cooking liquid to a boil. Add the pearl onions and button mushrooms and simmer over moderate heat until the mushrooms are tender, about 10 minutes. Add the veal and cook until the liquid has reduced to about 2 cups, about 10 minutes longer.
In a small bowl, whisk the egg yolks and cream until well blended. Gradually whisk the egg mixture into the stew and simmer gently until thickened, about 2 minutes. Stir in the noodles and season with salt and pepper. Serve hot.