Prepare the filling by finely chopping the leftover roast in a food processor together with an egg or two, lots of grated parmesan cheese and, if you like, a few spoonfuls of the leftover sugo (gravy) from the roast. Season, if need be, with salt and pepper to taste. (A bit of nutmeg is also nice.) Make sure the mixture is quite smooth and not too dry. If it is a bit too stiff, add another egg.
Meanwhile, you can make fresh pasta dough and cut it into rounds about 5 cm (3 in) in diameter—or do what I did tonight, and use some 'Hong Kong style dumpling wrappers', ready-made round disks of 'pasta'. Brush them lightly with some water to help them stick together and then place a heaping teaspoon of the filling in the center of each disk,
Fold the pasta disk over and then seal the round edge by pressing down firmly with your fingers, starting at the center and working your way to each end with both hands. (This helps avoid the filling oozing out.) Proceed until you have used up your ingredients.
You can cook your mezzelune right away, or let them dry a bit before using. If, however, they are to wait for more than a half hour or so, cover them with a towel to prevent them from drying out too much.
Bring abundant well salted water to a soft boil, then add your mezzelune (being careful not to mangle them!) to the boiling water. Adjust the heat so that they boil gently. Do not allow the water to come to rolling boil or they may break apart. Cook for only 2-4 minutes, depending on how long they have been waiting around.
When the mezzelune are done, scoop them out of the water with a large slotted spoon. You can dress them in a number of ways. Here are three possibilities: