Preheat the oven to 350 degrees F.
Heat 2 crepe pans over medium heat, smear with oil, ladle in 2 ounces of batter and cook the crespelle, 2 at a time until all batter is used.
In a 12-inch saute pan over a medium-high flame, heat the olive oil until hot but not smoking. Add the onion, carrot and celery, and cook until soft and golden brown, about 5 minutes. Add the chicken meat, livers, and nutmeg
. Season, to taste, with salt and pepper. Lower the heat to medium and let cook until the meat is browned, about 15 minutes. Remove from the heat and set aside to cool at room temperature.
When the meat mixture has cooled, add the eggs and 1/2 cup of Parmigiano. Use a wooden spoon to mix until well combined. Scoop 1 1/2 tablespoons of the meat mixture into the center of each crespella. Roll the crespella into a tube along the long side and place in a lightly oiled baking dish
, in a single layer, seal side down. Repeat with the remaining cannelloni, placing them side by side in the baking dish. Ladle the tomato sauce
over the cannelloni
. Sprinkle the crespelle with the remaining Parmigiano and bake in the oven until the cannelloni are hot throughout and the cheese
is hot and bubbling, about 30 minutes. Serve immediately on warmed plates.