In a large enameled cast-iron casserole, cover the veal with cold water. Bring to a simmer and cook for 2 minutes. Drain the veal and rinse it under cold water.
Wash out the casserole and return the meat to it. Add 8 cups of the stock, the large onion, garlic and bouquet garni and season with salt. Bring to a simmer, cover partially and simmer over moderate heat until the veal is very tender, about 1 hour and 15 minutes. Drain the veal; reserve the broth. Discard the onion, garlic and bouquet garni. Rinse out the casserole and return the meat to it.
Meanwhile, in a saucepan of boiling water, blanch the pearl onions for 30 seconds. Drain and transfer to a bowl of ice water. Drain again. Trim the roots and peel the onions.
In a skillet, melt 1 tablespoon of the butter. Add the pearl onions and remaining 1/2 cup of stock. Season with salt, cover and cook over low heat until the onions are tender, 30 minutes. Scatter the onions over the veal.
In a bowl, toss the mushrooms with the lemon juice. In a large saucepan, melt the remaining 4 tablespoons of butter over low heat. Add the flour and whisk until bubbling. Add 3 1/2 cups of the reserved veal broth and bring to a simmer, whisking constantly. Simmer over low heat, whisking frequently, until thickened, 10 minutes. Add the mushrooms, season with salt and white pepper and simmer over low heat for 10 minutes. Pour the mushrooms and sauce over the veal and add 2 tablespoons of the cream. Cover and simmer for 5 minutes, stirring occasionally.
In a medium heatproof bowl, whisk the yolks with the remaining 1/2 cup of cream; season with salt and white pepper. Gradually ladle in about 1 cup of the hot sauce from the stew, whisking. Pour the enriched sauce into the casserole and warm the stew over low heat, stirring gently, until thickened; do not let the sauce simmer. Stir in the parsley and serve with rice or fettuccine.