Here's a wonderful way to 'recycle' leftover brasato or other pot roast—as a filling for stuffed pasta:
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' (see Notes below). 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, (see photo above).
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.) (See photo at left.) 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:
Al burro e salvia: Perhaps the most common (and, to my mind, the best) way is to melt a good amount of butter (say 50g/2 oz per serving) in a skillet with some sage, allowing the sage to 'simmer' in the butter but not allowing the butter to color at all. Then add your mezzelune to the skillet, along with a bit of the pasta water and a bit of grated parmesan cheese. Toss together over medium heat very quickly and serve with additional parmesan on top.
Al sugo d'arrosto: If you have any gravy left over from the brasato, you can re-heat a bit of it in a skillet and toss the mezzelune in it. Serve with some grated parmesan on the side for those who want some.
Al sugo di pomodoro: You can also dress the mezzelune with a very simple sugo di pomodoro, known in the English-speaking world as a 'marinara sauce'.
These mezzelune are also very nice served in brodo, in homemade broth.
Mezzeluna al sugo d'arrosto
NOTES: Those round Hong Kong style dumpling wrappers were quite a discovery! I found them at H Mart, a Korean-owned Asian supermarket with branches all over the US and South Korea. (Besides these useful wrappers, they have excellent meats, fish and produce at very reasonable prices.) Another well known 'short cut' for making stuffed pasta is to use wonton wrappers, but I generally find these to be just a bit too fine for Italian pasta dishes; they tend to get overwhelmed by the stuffing and/or sauce (though I have used eggroll wrappers to make cannelloni with very satisfactory results). These dumpling wrappers, on the other hand, while still a bit too 'translucent' when cooked, are a nice golden yellow and a bit thicker, and have a rather firmer texture—in short, they look and react to cooking much more like real fresh egg pasta. (The looks are, however, partially deceiving: their yellow color actually comes from using Yellow Dyes #3 and 5...)
In Piemonte, where this dish originates, the usual pasta to be stuffed with this brasato filling is actually agnolotti (aka ravioli) a kind of square pasta. But since I had round pasta on hand, I used made them into another common stuffed pasta shape, the mezzaluna, or 'half moon', made by folding the pasta disk in half as described above. You can also make round ravioli by placing one disk on top of another—with the filling in between them, of course.
