Cut the veal and chicken into 1-inch pieces.
Melt the butter in a large saute pan over medium heat. When the foam begins to subside, add the veal with salt and pepper and brown it well on all sides. Lift it out to a plate.
Add the chicken to the pan with a little salt and pepper and cook briefly, only until it no longer looks raw. Move it to the plate with the veal.
Add the chopped onion to the pan and cook, stirring, until it turns a pale gold. Add celery and carrot and cook, stirring now and then, until tender. Scrape the vegetables and all pan juices into a bowl.
Chop the cooked veal and chicken very fine (knife or food processor). Add the minced meat to the bowl.
Add ricotta, the 1/2 cup Parmesan, marjoram, parsley, and egg yolk. Mix until smooth and evenly combined. Taste and adjust salt and pepper.
Remove any bruised outer lettuce leaves. Pull off the remaining leaves carefully and rinse gently in cold water. Save the very small inner leaves for another use.
Bring 1 gallon of water to a boil, add 1 tbsp (15 ml) salt, and blanch 3 or 4 lettuce leaves at a time for 5 to 6 seconds. Lift them out with a skimmer and spread them out to cool.
Spread one leaf flat and place 1 1/2 to 2 tbsp (25 to 30 ml) filling in the center. Fold the leaf into a neat package. Repeat with the remaining leaves and filling.
Tie each package securely with kitchen twine (do not use string that can melt).
Bring the broth to a slow simmer. Gently lower the lettuce bundles into the pot. If they are not fully covered, add water to cover by about 1 inch.
Cover and cook at a gentle simmer for about 20 minutes.
Turn off the heat, let the soup settle a few minutes, then lift out the bundles carefully.
Put one toast slice in each bowl, set a bundle on the toast, and ladle broth over it. Serve with additional grated Parmigiano.