Matchstick pieces are pieces of food which have been cut to be very small; they are often around the size of matchsticks, hence the name. There are a wide range of uses for matchstick pieces, from stir fries to salads; their small, even size makes them extremely versatile. Most commonly, matchstick pieces are cut from firm vegetables like carrots, although it is also possible to find meats cut into matchstick-like shreds.
There are several ways to make matchstick pieces. Many people achieve this small and precise cut by julienning food with a sharp knife. In a julienne cut, food is cut into extremely thin, even strips which can be cut into finer strips for the purpose of making matchstick pieces. An easier way of julienning vegetables involves the use of a mandoline slicer, a piece of kitchen equipment which slices the food for you as you feed it through. If you don't feel inclined to use a knife or a mandoline, some markets sell common vegetables which are pre-cut into matchstick pieces.
There are several reasons to use matchstick pieces in cooking. The first is that since the pieces are cut very small, they cook quickly. This can be convenient when throwing together a dish like a stir fry. The even size of matchstick pieces ensures that they cook evenly as well. They also add texture and structure to a dish; matchstick cut carrots, for example, can be thrown in at the last minute so that they retain their crunchiness and create some volume in the finished dish.
Some recipes call for everything to be cut into matchstick pieces; coleslaw, for example, is often made with uniformly julienne cut pieces of cabbage, carrot, and so forth. The even sizes help to promote an even distribution of the sauce, which can be helpful in something like coleslaw, where chunks of sauce would be rather unpleasant. Matchstick pieces can also be used as an accent.
If you're making matchstick pieces with a knife, rather than a mandoline, start by making lengthwise cuts at an even distance from each other. If you're working with a rounded food like a carrot or an onion, cut it in half so that it does not move around on the cutting board. As you make the lengthwise cuts, use your hand to keep the food together. Once you have finished a series of even cuts in one direction, creating a set of stacked layers, cut in the other direction to slice the layers into slivers. Use several cuts along the midlength of the food to turn the long slivers into matchsticks, and then use as desired.