Place veal in a 4-quart casserole. Add broth and bring to a boil. Skim all scum from surface. Reduce heat to low. Add carrot, leeks, celery and bouquet garni. Season with salt. Simmer 1 hour on very low heat. Add mushrooms and onions. Simmer 30 minutes more. Remove from heat and let rest for 30 minutes.
Remove meat and vegetables to a large bowl, draining well, discarding leeks and bouquet garni. Cover with plastic wrap. Strain cooking liquid into a separate bowl and clean pan. Return liquid to pan and reduce by half, about 5 minutes. Stir in cream. Simmer for 10 minutes, until slightly thickened. Beat egg yolks in a bowl and slowly beat in about half a cup sauce to warm yolks. Slowly whisk egg yolk mixture into pan, remove from heat and keep whisking until sauce has a creamy consistency. Add lemon juice and season with salt and pepper.
Return meat, celery, mushrooms and onions to pan. Slice carrots 1/2-inch thick and add. Bring barely to a simmer, stirring, just until ingredients are warmed through. Do not allow sauce to boil or egg yolks will curdle. Check seasonings, garnish with parsley and serve with rice.