1. You can use almost every left-over to stuff into your panzerotti. Clearly, there are fillings which are more Italian than others, but we're not picky.
2. Every member of your family can create his own favorite filling.
To make the concept clearer to you, I copy from Wikipedia (Mind you, the picture is mine, showing a glorious "Funghi and Salsiccia"-Panzerotto and a Fior di Zucca):
Panzarotti or panzerotti are filled pastries, different forms of which are popular in Italy and in the United States, especially in Southern New Jersey. Panzerotti originated in central and southern Italy, especially in Apulia. They are small versions of the calzone, but produced with a softer dough. The most common fillings are tomato and mozzarella, but spinach, mushrooms, baby corn, and ham are often used. Another filling is onions stir fried in olive oil and seasoned with salted anchovies and capers, a seasoning that, mixed with bread, is also used in Apulia for stuffed bell peppers.In America the word has come to be spelled "panzarotti", and is regarded as singular (with the plural being "panzarotties" or "panzarotti"). They can come in various sizes from 4" to 12", and are most commonly semi-circular shaped. It consists of a pocket of dough filled with varying amounts of melted mozzarella cheese, tomato sauce, and any reasonable number of fillings, which is then wrapped, salted, and deep-fried. The panzarotti rises during this process, creating a pocket containing a considerable amount of steam which should be partially released prior to eating.Enough babbling, on to the real thing!!!
Ingredients:- one ball of yeast-dough (basically the same you'd make for white bread or pizza: flour, water, yeast, sugar for the yeast to rise, a bit of olive-oil, salt)
- fillings as you like, the classic is tomato-sauce and mozzarella-cheese
- sunflower-seed oil for the frying (or equivalent)
For the fillings I prepared and then mixed freely:Spicy salami in little chunks
Italian salsiccia
Funghi
Tomato-sauce (tomatos, olive-oil, basil; let simmer for a while and then cool off)
Mozzarella-cheese in little chunks
Fior di Zucca (it's the flower of zucchini! You see it here on the left side and above.)
After the dough has risen for the appropriate time you can start preparing the Panzerotti. As quoted above, there's no rule as to the size, but they're often served as antipasto so I wouldn't make them too big. Take a piece of dough, shape it into a ball and roll it flat out. You should obtain a flat and round piece of dough, like a mini-pizza. 
Careful not to roll it out too thin as it might tear when closing it. I have a Panzerotti-shaper, so I transfer the piece onto it and then add the filling. Don't use too much filling and leave a "filling-free" border. Close carefully, pressing firmly down on the borders. 
It should look like this, but it could also look a lot better! You then heat the oil in a frying pan and just let the panzerotti fry in it, flipping it over after some time. Again, I'm sorry not to be able to give an exact time, but you'll figure it out. 
Mine were slightly too browned, I'll try not to heat the oil too much the next time and to cook them a bit slower - well I was hungry while cooking and wanted them to be ready quicklyquicklyquickly....And here are two more fillings, one is tomato-salami-mozzarella and the other is zucchini-flower and mozzarella (this one was especially yummy!!)
