Heat olive oil in a large, heavy-bottomed pot over medium-high heat. Cook and stir celery, onion, and garlic in hot oil until translucent, about 5 minutes.
Add pork and chicken and cook for 7 to 10 minutes.
Combine tomato puree and tomato paste with 1 cup water, and add to meat mixture. Reduce heat to low and cook, stirring occasionally, for 2 hours, or until pork and chicken are falling off the bone.
Remove meat from the pot to cool, and set sauce aside.
Meanwhile, remove olive pits using a special olive pitting tool. Make a slit in one side of each olive large enough to insert stuffing.
Once cooled, remove pork and chicken meat from the bones, and mince.
Mix together with 2 beaten eggs, Parmesan cheese, ground nutmeg, lemon zest, and 1/4 cup of reserved sauce. Use more or less sauce as needed so that meat mixture is moist, but not too wet.
Fill each olive with enough stuffing so that a small amount is pushing out of the slit. Dip each stuffed olive in flour, then beaten egg, then bread crumbs. Stuffed olives may be frozen in an air-tight container at this point until ready to use.
Heat oil in deep-fryer to 375 degrees F (190 degrees C).
Fry olives in hot oil for about 3 minutes, or until golden brown on the outside.
