In a large Dutch oven over high heat, bring the veal, water, and salt to a boil, then reduce to a simmer and cook for 30 minutes. Skim any scum as it forms and discard.
Add the celery, clove-studded onion, carrots, thyme, and bay leaf, and continue to let the veal cook slowly for another hour until it is very tender.
While the veal is cooking, trim the mushrooms and cut into quarters. Melt 2 tablespoons of butter in a skillet, add the mushrooms, season lightly with salt, and cook gently for 3 minutes — do not brown. Add the lemon juice and half a ladle of the veal broth and cook for 5 minutes or until soft. Set aside.
When the veal is tender, pour the meat and vegetables into a colander, reserving the broth. Discard the celery, onion, thyme and bay, but keep the veal and carrots.
Melt the remaining butter in the same Dutch oven (no need to wash it) over low heat. Add the flour and cook gently for 2-3 minutes when melted. Slowly add the reserved veal broth to the flour mixture, whisking constantly. Season lightly with salt and generously with white pepper. Bring to a boil, then return the meat and carrots to the pot along with the reserved mushrooms.
Whisk together the egg yolks and cream in a separate bowl, then pour into the stew in a steady stream while stirring. Immediately turn off the heat. The consistency should be that of a light stew, not overly thick.
Sprinkle cilantro leaves over and serve immediately with rice.