Trim the celery stalks of their top shoots and any leaves, as well as their root ends. Then cut them into 8-10cm (3-4 inch) lengths.
Parboil the pieces in well salted water until tender but not mushy, usually anywhere between 5-10 minutes depending on the size and quality of your celery.
Set aside on a dish towel to dry and cool completely.
Prepare the filling
In a mixing bowl, place the ground veal, minced mortadella and the rest of the filling ingredients other than the egg. Knead well with washed hands, then knead in the egg as well until it is completely absorbed. Keep kneading until the mixture is compact and uniform.
Taste and adjust for seasoning. The filling should be very savory.
Stuffing the celery
Take a celery piece, then heap on a good dollop of the veal mixture, enough to fill the cavity and then some. Spread it out evenly along the length of the piece, pressing it into the cavity, then place another celery piece of the same width on top. Press together to form a little slightly overstuffed "log", like so:
Repeat until you've used up all the celery and/or stuffing.
Batter and fry the stuffed celery
Fill a skillet or sauté pan with oil about cm (inch) high. Set over a lively flame.
Roll the stuffed celery logs in flour.
When the oil is quite hot, dip the celery logs in the beaten egg and then transfer them immediately to the skillet. Fry them over a lively flame, turning them gingerly from time to time, until nice and golden brown on all sides.
Simmer
Meanwhile, bring your sugo di carne to a simmer in another skillet or sauté pan with a small glassful of water.
As the celery logs are done frying, transfer them to the pan with the sugo. Let them simmer in the sugo, turning them from time to time and adding more water if the sauce gets too thick,, until they have taken on a lovely dark red hue from the sugo and have totally cooked through, about 5 minutes or so.
Serve
Serve still hot, napped with some of the sugo and, if you like, sprinkled with grated cheese.
Notes
For a lighter dish, substiute a simple tomato sauce or broth for the meat sauce